Reverse Mathematics: Proofs from the Inside Out
John Stillwell - 2018
https://www.amazon.com/dp/0691177171

A review intro:

"Reverse mathematics is a programme in mathematical logic,
initiated in the mid-1970s, which seeks to determine which
axioms are necessary to prove theorems in areas of ordinary
mathematics such as real analysis, countable abstract algebra,
countably infinite combinatorics, and the topology of complete
separable metric spaces. Reverse Mathematics: Proofs From
the Inside Out is the first popular book on the subject, aimed at
advanced undergraduates in mathematics, but also a good introduction
for philosophers of mathematics. The time is certainly ripe for such
a book, bringing this fascinating area of contemporary mathematical
logic to a broader audience."

Review of John Stillwell,
Reverse Mathematics: Proofs from the Inside Out
Benedict Eastaugh∗ benedict@eastaugh.net
22 November, 2019
https://extralogical.net/files/stillwell-review.pdf

Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> Reverse Mathematics: Proofs from the Inside Out
> John Stillwell - 2018
> https://www.amazon.com/dp/0691177171

On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> A review intro:
>
> "Reverse mathematics is a programme in mathematical logic,
> initiated in the mid-1970s, which seeks to determine which
> axioms are necessary to prove theorems in areas of ordinary
> mathematics such as real analysis, countable abstract algebra,
> countably infinite combinatorics, and the topology of complete
> separable metric spaces. Reverse Mathematics: Proofs From
> the Inside Out is the first popular book on the subject, aimed at
> advanced undergraduates in mathematics, but also a good introduction
> for philosophers of mathematics. The time is certainly ripe for such
> a book, bringing this fascinating area of contemporary mathematical
> logic to a broader audience."
>
> Review of John Stillwell,
> Reverse Mathematics: Proofs from the Inside Out
> Benedict Eastaugh∗ bene...@eastaugh.net
> 22 November, 2019
> https://extralogical.net/files/stillwell-review.pdf
> Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > Reverse Mathematics: Proofs from the Inside Out
> > John Stillwell - 2018
> > https://www.amazon.com/dp/0691177171

Ant dance

Uh, it makes sense to have reverse mathematics,
"adopting small theories", where, something like
ZF set theory and definition, has for example
"usual proofs that don't contradict other usual proofs
of the same objects in theory". I.e. a weak theory,
missing a case, is broken.

Then forward is toward a model of all knowledge.

Which for example have reverse mathematics as tiny
fragments, is having the theorems under domains if
they're going to be logical.

Reverse Mathematics already went to the masses.

Herpes boys english is from reverse mathematics.
Nobody understands it, its too minimal. LMAO!

Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > A review intro:
> >
> > "Reverse mathematics is a programme in mathematical logic,
> > initiated in the mid-1970s, which seeks to determine which
> > axioms are necessary to prove theorems in areas of ordinary
> > mathematics such as real analysis, countable abstract algebra,
> > countably infinite combinatorics, and the topology of complete
> > separable metric spaces. Reverse Mathematics: Proofs From
> > the Inside Out is the first popular book on the subject, aimed at
> > advanced undergraduates in mathematics, but also a good introduction
> > for philosophers of mathematics. The time is certainly ripe for such
> > a book, bringing this fascinating area of contemporary mathematical
> > logic to a broader audience."
> >
> > Review of John Stillwell,
> > Reverse Mathematics: Proofs from the Inside Out
> > Benedict Eastaugh∗ bene...@eastaugh.net
> > 22 November, 2019
> > https://extralogical.net/files/stillwell-review.pdf
> > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > Reverse Mathematics: Proofs from the Inside Out
> > > John Stillwell - 2018
> > > https://www.amazon.com/dp/0691177171
> Ant dance
>
> Uh, it makes sense to have reverse mathematics,
> "adopting small theories", where, something like
> ZF set theory and definition, has for example
> "usual proofs that don't contradict other usual proofs
> of the same objects in theory". I.e. a weak theory,
> missing a case, is broken.
>
> Then forward is toward a model of all knowledge.
>
> Which for example have reverse mathematics as tiny
> fragments, is having the theorems under domains if
> they're going to be logical.
>
> Reverse Mathematics already went to the masses.

On Monday, September 13, 2021 at 5:48:24 PM UTC-7, Mostowski Collapse wrote:
> Herpes boys english is from reverse mathematics.
> Nobody understands it, its too minimal. LMAO!
> Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> > On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > > A review intro:
> > >
> > > "Reverse mathematics is a programme in mathematical logic,
> > > initiated in the mid-1970s, which seeks to determine which
> > > axioms are necessary to prove theorems in areas of ordinary
> > > mathematics such as real analysis, countable abstract algebra,
> > > countably infinite combinatorics, and the topology of complete
> > > separable metric spaces. Reverse Mathematics: Proofs From
> > > the Inside Out is the first popular book on the subject, aimed at
> > > advanced undergraduates in mathematics, but also a good introduction
> > > for philosophers of mathematics. The time is certainly ripe for such
> > > a book, bringing this fascinating area of contemporary mathematical
> > > logic to a broader audience."
> > >
> > > Review of John Stillwell,
> > > Reverse Mathematics: Proofs from the Inside Out
> > > Benedict Eastaugh∗ bene...@eastaugh.net
> > > 22 November, 2019
> > > https://extralogical.net/files/stillwell-review.pdf
> > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > > Reverse Mathematics: Proofs from the Inside Out
> > > > John Stillwell - 2018
> > > > https://www.amazon.com/dp/0691177171
> > Ant dance
> >
> > Uh, it makes sense to have reverse mathematics,
> > "adopting small theories", where, something like
> > ZF set theory and definition, has for example
> > "usual proofs that don't contradict other usual proofs
> > of the same objects in theory". I.e. a weak theory,
> > missing a case, is broken.
> >
> > Then forward is toward a model of all knowledge.
> >
> > Which for example have reverse mathematics as tiny
> > fragments, is having the theorems under domains if
> > they're going to be logical.
> >
> > Reverse Mathematics already went to the masses.

Put it all together...

Each one a hit!

Every time herpes boy pushes the submit button:

Godzilla had a stroke trying to read this and fricking died
https://imgflip.com/memegenerator/254097096/Godzilla-had-a-stroke-trying-to-read-this-and-fricking-died

LoL

Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 02:48:24 UTC+2:
> Herpes boys english is from reverse mathematics.
> Nobody understands it, its too minimal. LMAO!
> Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> > On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > > A review intro:
> > >
> > > "Reverse mathematics is a programme in mathematical logic,
> > > initiated in the mid-1970s, which seeks to determine which
> > > axioms are necessary to prove theorems in areas of ordinary
> > > mathematics such as real analysis, countable abstract algebra,
> > > countably infinite combinatorics, and the topology of complete
> > > separable metric spaces. Reverse Mathematics: Proofs From
> > > the Inside Out is the first popular book on the subject, aimed at
> > > advanced undergraduates in mathematics, but also a good introduction
> > > for philosophers of mathematics. The time is certainly ripe for such
> > > a book, bringing this fascinating area of contemporary mathematical
> > > logic to a broader audience."
> > >
> > > Review of John Stillwell,
> > > Reverse Mathematics: Proofs from the Inside Out
> > > Benedict Eastaugh∗ bene...@eastaugh.net
> > > 22 November, 2019
> > > https://extralogical.net/files/stillwell-review.pdf
> > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > > Reverse Mathematics: Proofs from the Inside Out
> > > > John Stillwell - 2018
> > > > https://www.amazon.com/dp/0691177171
> > Ant dance
> >
> > Uh, it makes sense to have reverse mathematics,
> > "adopting small theories", where, something like
> > ZF set theory and definition, has for example
> > "usual proofs that don't contradict other usual proofs
> > of the same objects in theory". I.e. a weak theory,
> > missing a case, is broken.
> >
> > Then forward is toward a model of all knowledge.
> >
> > Which for example have reverse mathematics as tiny
> > fragments, is having the theorems under domains if
> > they're going to be logical.
> >
> > Reverse Mathematics already went to the masses.

On Monday, September 13, 2021 at 5:51:58 PM UTC-7, Mostowski Collapse wrote:
> Every time herpes boy pushes the submit button:
>
> Godzilla had a stroke trying to read this and fricking died
> https://imgflip.com/memegenerator/254097096/Godzilla-had-a-stroke-trying-to-read-this-and-fricking-died
>
> LoL
> Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 02:48:24 UTC+2:
> > Herpes boys english is from reverse mathematics.
> > Nobody understands it, its too minimal. LMAO!
> > Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> > > On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > > > A review intro:
> > > >
> > > > "Reverse mathematics is a programme in mathematical logic,
> > > > initiated in the mid-1970s, which seeks to determine which
> > > > axioms are necessary to prove theorems in areas of ordinary
> > > > mathematics such as real analysis, countable abstract algebra,
> > > > countably infinite combinatorics, and the topology of complete
> > > > separable metric spaces. Reverse Mathematics: Proofs From
> > > > the Inside Out is the first popular book on the subject, aimed at
> > > > advanced undergraduates in mathematics, but also a good introduction
> > > > for philosophers of mathematics. The time is certainly ripe for such
> > > > a book, bringing this fascinating area of contemporary mathematical
> > > > logic to a broader audience."
> > > >
> > > > Review of John Stillwell,
> > > > Reverse Mathematics: Proofs from the Inside Out
> > > > Benedict Eastaugh∗ bene...@eastaugh.net
> > > > 22 November, 2019
> > > > https://extralogical.net/files/stillwell-review.pdf
> > > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > John Stillwell - 2018
> > > > > https://www.amazon.com/dp/0691177171
> > > Ant dance
> > >
> > > Uh, it makes sense to have reverse mathematics,
> > > "adopting small theories", where, something like
> > > ZF set theory and definition, has for example
> > > "usual proofs that don't contradict other usual proofs
> > > of the same objects in theory". I.e. a weak theory,
> > > missing a case, is broken.
> > >
> > > Then forward is toward a model of all knowledge.
> > >
> > > Which for example have reverse mathematics as tiny
> > > fragments, is having the theorems under domains if
> > > they're going to be logical.
> > >
> > > Reverse Mathematics already went to the masses.

Lot easier to carry a point when there isn't another.

With gibberish like "usual proofs that don't contradict other usual proofs
of the same objects in theory", you can kill 10 Godzillas in a row.

Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 22:56:55 UTC+2:
> On Monday, September 13, 2021 at 5:51:58 PM UTC-7, Mostowski Collapse wrote:
> > Every time herpes boy pushes the submit button:
> >
> > Godzilla had a stroke trying to read this and fricking died
> > https://imgflip.com/memegenerator/254097096/Godzilla-had-a-stroke-trying-to-read-this-and-fricking-died
> >
> > LoL
> > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 02:48:24 UTC+2:
> > > Herpes boys english is from reverse mathematics.
> > > Nobody understands it, its too minimal. LMAO!
> > > Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> > > > On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > > > > A review intro:
> > > > >
> > > > > "Reverse mathematics is a programme in mathematical logic,
> > > > > initiated in the mid-1970s, which seeks to determine which
> > > > > axioms are necessary to prove theorems in areas of ordinary
> > > > > mathematics such as real analysis, countable abstract algebra,
> > > > > countably infinite combinatorics, and the topology of complete
> > > > > separable metric spaces. Reverse Mathematics: Proofs From
> > > > > the Inside Out is the first popular book on the subject, aimed at
> > > > > advanced undergraduates in mathematics, but also a good introduction
> > > > > for philosophers of mathematics. The time is certainly ripe for such
> > > > > a book, bringing this fascinating area of contemporary mathematical
> > > > > logic to a broader audience."
> > > > >
> > > > > Review of John Stillwell,
> > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > Benedict Eastaugh∗ bene...@eastaugh.net
> > > > > 22 November, 2019
> > > > > https://extralogical.net/files/stillwell-review.pdf
> > > > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > > John Stillwell - 2018
> > > > > > https://www.amazon.com/dp/0691177171
> > > > Ant dance
> > > >
> > > > Uh, it makes sense to have reverse mathematics,
> > > > "adopting small theories", where, something like
> > > > ZF set theory and definition, has for example
> > > > "usual proofs that don't contradict other usual proofs
> > > > of the same objects in theory". I.e. a weak theory,
> > > > missing a case, is broken.
> > > >
> > > > Then forward is toward a model of all knowledge.
> > > >
> > > > Which for example have reverse mathematics as tiny
> > > > fragments, is having the theorems under domains if
> > > > they're going to be logical.
> > > >
> > > > Reverse Mathematics already went to the masses.
> Lot easier to carry a point when there isn't another.

Probably a form of Autism, only you dont know it yet.

Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 23:45:31 UTC+2:
> With gibberish like "usual proofs that don't contradict other usual proofs
> of the same objects in theory", you can kill 10 Godzillas in a row.
> Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 22:56:55 UTC+2:
> > On Monday, September 13, 2021 at 5:51:58 PM UTC-7, Mostowski Collapse wrote:
> > > Every time herpes boy pushes the submit button:
> > >
> > > Godzilla had a stroke trying to read this and fricking died
> > > https://imgflip.com/memegenerator/254097096/Godzilla-had-a-stroke-trying-to-read-this-and-fricking-died
> > >
> > > LoL
> > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 02:48:24 UTC+2:
> > > > Herpes boys english is from reverse mathematics.
> > > > Nobody understands it, its too minimal. LMAO!
> > > > Ross A. Finlayson schrieb am Dienstag, 14. September 2021 um 02:38:08 UTC+2:
> > > > > On Monday, September 13, 2021 at 5:29:59 PM UTC-7, Mostowski Collapse wrote:
> > > > > > A review intro:
> > > > > >
> > > > > > "Reverse mathematics is a programme in mathematical logic,
> > > > > > initiated in the mid-1970s, which seeks to determine which
> > > > > > axioms are necessary to prove theorems in areas of ordinary
> > > > > > mathematics such as real analysis, countable abstract algebra,
> > > > > > countably infinite combinatorics, and the topology of complete
> > > > > > separable metric spaces. Reverse Mathematics: Proofs From
> > > > > > the Inside Out is the first popular book on the subject, aimed at
> > > > > > advanced undergraduates in mathematics, but also a good introduction
> > > > > > for philosophers of mathematics. The time is certainly ripe for such
> > > > > > a book, bringing this fascinating area of contemporary mathematical
> > > > > > logic to a broader audience."
> > > > > >
> > > > > > Review of John Stillwell,
> > > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > > Benedict Eastaugh∗ bene...@eastaugh.net
> > > > > > 22 November, 2019
> > > > > > https://extralogical.net/files/stillwell-review.pdf
> > > > > > Mostowski Collapse schrieb am Dienstag, 14. September 2021 um 01:30:46 UTC+2:
> > > > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > > > John Stillwell - 2018
> > > > > > > https://www.amazon.com/dp/0691177171
> > > > > Ant dance
> > > > >
> > > > > Uh, it makes sense to have reverse mathematics,
> > > > > "adopting small theories", where, something like
> > > > > ZF set theory and definition, has for example
> > > > > "usual proofs that don't contradict other usual proofs
> > > > > of the same objects in theory". I.e. a weak theory,
> > > > > missing a case, is broken.
> > > > >
> > > > > Then forward is toward a model of all knowledge.
> > > > >
> > > > > Which for example have reverse mathematics as tiny
> > > > > fragments, is having the theorems under domains if
> > > > > they're going to be logical.
> > > > >
> > > > > Reverse Mathematics already went to the masses.
> > Lot easier to carry a point when there isn't another.

On Tuesday, September 14, 2021 at 1:30:46 AM UTC+2, Mostowski Collapse wrote:
> Reverse Mathematics: Proofs from the Inside Out
> John Stillwell - 2018
> https://www.amazon.com/dp/0691177171

http://libgen.rs/search.php?req=reverse+mathematics&open=0&res=25&view=simple&phrase=1&column=def

On Tuesday, September 14, 2021 at 5:13:18 PM UTC-7, sobriquet wrote:
> On Tuesday, September 14, 2021 at 1:30:46 AM UTC+2, Mostowski Collapse wrote:
> > Reverse Mathematics: Proofs from the Inside Out
> > John Stillwell - 2018
> > https://www.amazon.com/dp/0691177171
> http://libgen.rs/search.php?req=reverse+mathematics&open=0&res=25&view=simple&phrase=1&column=def

"School of Simpson"

Basically Woodin, Simpson, Nelson, ..., euh, after Jech,
with determinacy or the simpler or the inner,
since Cohen, Feferman, ..., into category theory,
about Brentano, the, "Reverse Mathematics" is just
for making what compiles down to a truth-table evaluator
is smaller: it's the opposite of the dialectic the result,
though the deliberation itself is of course dialectic.

These are schools.

On Thursday, September 16, 2021 at 6:36:59 PM UTC-7, Ross A. Finlayson wrote:
> On Tuesday, September 14, 2021 at 5:13:18 PM UTC-7, sobriquet wrote:
> > On Tuesday, September 14, 2021 at 1:30:46 AM UTC+2, Mostowski Collapse wrote:
> > > Reverse Mathematics: Proofs from the Inside Out
> > > John Stillwell - 2018
> > > https://www.amazon.com/dp/0691177171
> > http://libgen.rs/search.php?req=reverse+mathematics&open=0&res=25&view=simple&phrase=1&column=def
> "School of Simpson"
>
> Basically Woodin, Simpson, Nelson, ..., euh, after Jech,
> with determinacy or the simpler or the inner,
> since Cohen, Feferman, ..., into category theory,
> about Brentano, the, "Reverse Mathematics" is just
> for making what compiles down to a truth-table evaluator
> is smaller: it's the opposite of the dialectic the result,
> though the deliberation itself is of course dialectic.
>
> These are schools.

(Mostly the school is Scott, Sheffer, ..., Gentzen and so on.)

On Thursday, September 16, 2021 at 7:49:15 PM UTC-7, Ross A. Finlayson wrote:
> On Thursday, September 16, 2021 at 6:36:59 PM UTC-7, Ross A. Finlayson wrote:
> > On Tuesday, September 14, 2021 at 5:13:18 PM UTC-7, sobriquet wrote:
> > > On Tuesday, September 14, 2021 at 1:30:46 AM UTC+2, Mostowski Collapse wrote:
> > > > Reverse Mathematics: Proofs from the Inside Out
> > > > John Stillwell - 2018
> > > > https://www.amazon.com/dp/0691177171
> > > http://libgen.rs/search.php?req=reverse+mathematics&open=0&res=25&view=simple&phrase=1&column=def
> > "School of Simpson"
> >
> > Basically Woodin, Simpson, Nelson, ..., euh, after Jech,
> > with determinacy or the simpler or the inner,
> > since Cohen, Feferman, ..., into category theory,
> > about Brentano, the, "Reverse Mathematics" is just
> > for making what compiles down to a truth-table evaluator
> > is smaller: it's the opposite of the dialectic the result,
> > though the deliberation itself is of course dialectic.
> >
> > These are schools.
> (Mostly the school is Scott, Sheffer, ..., Gentzen and so on.)

"The first topologies defined on a lattice directly from the
lattice ordering (that is, Birkhoff's order topology and Frink's
interval topology) involved "symmetrical" definitions -- the
topologies assigned to L and to L_op were identical. The guiding
example was always the unit interval of real numbers in its natural
order, which is of course a highly symmetrical lattice. The initial interest
was in such questions as which lattices became compact and/or Hausdorff
in these topologies. The Scott topology stands in strong contrast to such
an approach. Indieed it is a "one-way" topology, since, for example, all the
open sets are always upper sets; thus, for nontrivial lattices, the T_0-
separation axiom is the strongest it satisfies. Nevertheless, we saw in
Chapter II that the Scott topology provides many links between continuous
lattices and general topology in such classical areas as the theory of
semicontinuous functions and in the study of lattices of closed (compact,
convex) sets (ideals) in many familiar structures."
-- A Compendium of Continuous Lattices

https://www.springer.com/gp/book/9783642676802

Here for example the authors have organized five and six usual topologies
about the unit interval, for example about Hausdorff and Frink and Birkhoff
and Scott and Lawson and other "natural" topologies, assigning geometry to
Hausdorff and closure under category to Lawson. (And Birkhoff, Frink, and Scott,
and Hausdorff, and other usual natural topologies about the real numbers 0-1.)

Sometimes it's easier to keep track of names than all what they represent,
indicating related results, and for example a usual shared notation.

Also it helps when the same names wrote the book.

On Thursday, September 16, 2021 at 8:03:25 PM UTC-7, Ross A. Finlayson wrote:
> On Thursday, September 16, 2021 at 7:49:15 PM UTC-7, Ross A. Finlayson wrote:
> > On Thursday, September 16, 2021 at 6:36:59 PM UTC-7, Ross A. Finlayson wrote:
> > > On Tuesday, September 14, 2021 at 5:13:18 PM UTC-7, sobriquet wrote:
> > > > On Tuesday, September 14, 2021 at 1:30:46 AM UTC+2, Mostowski Collapse wrote:
> > > > > Reverse Mathematics: Proofs from the Inside Out
> > > > > John Stillwell - 2018
> > > > > https://www.amazon.com/dp/0691177171
> > > > http://libgen.rs/search.php?req=reverse+mathematics&open=0&res=25&view=simple&phrase=1&column=def
> > > "School of Simpson"
> > >
> > > Basically Woodin, Simpson, Nelson, ..., euh, after Jech,
> > > with determinacy or the simpler or the inner,
> > > since Cohen, Feferman, ..., into category theory,
> > > about Brentano, the, "Reverse Mathematics" is just
> > > for making what compiles down to a truth-table evaluator
> > > is smaller: it's the opposite of the dialectic the result,
> > > though the deliberation itself is of course dialectic.
> > >
> > > These are schools.
> > (Mostly the school is Scott, Sheffer, ..., Gentzen and so on.)
> "The first topologies defined on a lattice directly from the
> lattice ordering (that is, Birkhoff's order topology and Frink's
> interval topology) involved "symmetrical" definitions -- the
> topologies assigned to L and to L_op were identical. The guiding
> example was always the unit interval of real numbers in its natural
> order, which is of course a highly symmetrical lattice. The initial interest
> was in such questions as which lattices became compact and/or Hausdorff
> in these topologies. The Scott topology stands in strong contrast to such
> an approach. Indieed it is a "one-way" topology, since, for example, all the
> open sets are always upper sets; thus, for nontrivial lattices, the T_0-
> separation axiom is the strongest it satisfies. Nevertheless, we saw in
> Chapter II that the Scott topology provides many links between continuous
> lattices and general topology in such classical areas as the theory of
> semicontinuous functions and in the study of lattices of closed (compact,
> convex) sets (ideals) in many familiar structures."
> -- A Compendium of Continuous Lattices
>
>
> https://www.springer.com/gp/book/9783642676802
>
> Here for example the authors have organized five and six usual topologies
> about the unit interval, for example about Hausdorff and Frink and Birkhoff
> and Scott and Lawson and other "natural" topologies, assigning geometry to
> Hausdorff and closure under category to Lawson. (And Birkhoff, Frink, and Scott,
> and Hausdorff, and other usual natural topologies about the real numbers 0-1.)
>
> Sometimes it's easier to keep track of names than all what they represent,
> indicating related results, and for example a usual shared notation.
>
> Also it helps when the same names wrote the book.

https://www.uni-goettingen.de/de/document/download/07769c2a15f0bfbc24991e7dac4ada66.pdf/Gentzen.pdf
"From Hilbert to Gentzen and beyond", Reinhard Kahle, 2016

Here someone's written a neat formulary.

Of course there are various logics in forms, what for some modes,
are most concise and even provably most concise, that in the general,
there's much to be said for a usual body of common knowledge.

That of course is very technical and professional,
compared to the usual logical needs of mathematicians,
or the usual logical needs of people.

Where of course classical logic is all perfectly valid and so on...,
that's the point, it's logical.

Thank you!

AP brain farto mute for more than 14 hours? What happened?
Dont worry, if AP brain farto is not posting his nonsense, then
Ross A Finlayson aka herpes boy will post irrelevant nonsense.

Ross A. Finlayson schrieb am Freitag, 17. September 2021 um 05:31:25 UTC+2:
> ... irrelevant gibberish, not relevant to reverse mathematics ...

On Friday, September 17, 2021 at 10:09:03 AM UTC-7, Mostowski Collapse wrote:
> AP brain farto mute for more than 14 hours? What happened?
> Dont worry, if AP brain farto is not posting his nonsense, then
> Ross A Finlayson aka herpes boy will post irrelevant nonsense.
>
> Ross A. Finlayson schrieb am Freitag, 17. September 2021 um 05:31:25 UTC+2:
> > ... irrelevant gibberish, not relevant to reverse mathematics ...

The point is that Reverse Mathematics isn't much relevant to
mathematics except forward mathematics. (And simpler calculators.)

Please rest assured that only Burse has cold sores on his mind.

Then, for Simpson school is also a lot of work in ordinals,
all most always usually conservative thus mute in extension,
a study of a fragment of ZFC.

Still more irrelevant gibberish by herpes boy.

Ross A. Finlayson schrieb am Montag, 20. September 2021 um 04:11:01 UTC+2:
> On Friday, September 17, 2021 at 10:09:03 AM UTC-7, Mostowski Collapse wrote:
> > AP brain farto mute for more than 14 hours? What happened?
> > Dont worry, if AP brain farto is not posting his nonsense, then
> > Ross A Finlayson aka herpes boy will post irrelevant nonsense.
> >
> > Ross A. Finlayson schrieb am Freitag, 17. September 2021 um 05:31:25 UTC+2:
> > > ... irrelevant gibberish, not relevant to reverse mathematics ...
> The point is that Reverse Mathematics isn't much relevant to
> mathematics except forward mathematics. (And simpler calculators.)
>
> Please rest assured that only Burse has cold sores on his mind.
>
> Then, for Simpson school is also a lot of work in ordinals,
> all most always usually conservative thus mute in extension,
> a study of a fragment of ZFC.

I am still amazed how a grown up like Ross A Finlayson
can produce that much gibberish. He would only need
to open the first page of Stillwell to get introduction

what Reverse Mathematics is:

> Reverse Mathematics: Proofs from the Inside Out
> John Stillwell - 2018
> https://www.amazon.com/dp/0691177171

The booklet is a little thin and less mathematics more
prose. But mostly he can explain the quest of reverse
mathematics very well.

Mostowski Collapse schrieb am Montag, 20. September 2021 um 09:24:15 UTC+2:
> Still more irrelevant gibberish by herpes boy.
> Ross A. Finlayson schrieb am Montag, 20. September 2021 um 04:11:01 UTC+2:
> > On Friday, September 17, 2021 at 10:09:03 AM UTC-7, Mostowski Collapse wrote:
> > > AP brain farto mute for more than 14 hours? What happened?
> > > Dont worry, if AP brain farto is not posting his nonsense, then
> > > Ross A Finlayson aka herpes boy will post irrelevant nonsense.
> > >
> > > Ross A. Finlayson schrieb am Freitag, 17. September 2021 um 05:31:25 UTC+2:
> > > > ... irrelevant gibberish, not relevant to reverse mathematics ...
> > The point is that Reverse Mathematics isn't much relevant to
> > mathematics except forward mathematics. (And simpler calculators.)
> >
> > Please rest assured that only Burse has cold sores on his mind.
> >
> > Then, for Simpson school is also a lot of work in ordinals,
> > all most always usually conservative thus mute in extension,
> > a study of a fragment of ZFC.