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Re: Languages of Primitive Recusrive Arithmetic

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Subject: Re: Languages of Primitive Recusrive Arithmetic
Newsgroups: sci.logic
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From: ross.a.f...@gmail.com (Ross Finlayson)
Date: Fri, 9 Feb 2024 10:18:08 -0800
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by: Ross Finlayson - Fri, 9 Feb 2024 18:18 UTC

On 09/26/2015 10:29 AM, Ross A. Finlayson wrote:
>
>
> Seems a similar distinction as
> Presburger and Peano Arithmetic,
> and PRA (recursive) building out the
> bounds and product space as
> Presburger does under what are
> equivalent forms, of the arithmetic
> products of the closures of the
> spaces of the elements under their
> operations (or functions to self).
>
> So, like Presburger is "incomplete"
> as arithmetic (but second order
> around it is Peano arithmetic,
> complete), PRA has structures that
> model (build) an inductive set, for
> writing out each functional relation
> as a theorem. In the second order
> domains are defined for generally
> functions between domains besides
> functions intra-domain: "operators".
>

You know you wonder sometimes about how
a deconstructive approach to arithmetic
results how the usual modern algebra's
fully-assembled-field is really only
after having like an additive group
and a division ring, helping explain
why it's relevant that these approaches
that result models of the same objects
_including their closures_, are not
having the same closures, though,
helping explain why "long subtraction"
is a thing.

"If it ain't broke, don't fix it." -- Bert Lantz

tech / sci.logic / Re: Languages of Primitive Recusrive Arithmetic

Subject	Author
Re: Languages of Primitive Recusrive Arithmetic	Ross Finlayson