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tech / sci.logic / Re: Formal Definition of Set

Re: Formal Definition of Set

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Subject: Re: Formal Definition of Set
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From: ross.a.f...@gmail.com (Ross Finlayson)
Date: Fri, 9 Feb 2024 10:15:54 -0800
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by: Ross Finlayson - Fri, 9 Feb 2024 18:15 UTC

On 06/01/2015 06:28 PM, Ross A. Finlayson wrote:
> I think you are saying that
> set is the default return
> type of the function
> relation(), but to be only
> sets they are only sets,
> for any non-transitive
> property.
>
> Also the function and
> relation is only a set
> in set theory.
>
> They are the theories'
> objects or class definition.
>

This was sort of interesting.

Re: Formal Definition of Set

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Subject: Re: Formal Definition of Set
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From: ross.a.f...@gmail.com (Ross Finlayson)
Date: Wed, 21 Feb 2024 12:06:50 -0800
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by: Ross Finlayson - Wed, 21 Feb 2024 20:06 UTC

Set/class distinction, set/part distinction, ordinal/set distinction,
number vis-a-vis counting, reflects that the objects of arithmetic and
algebra, at once do and don't make extensionality, in the inner and
outer arithmetic and algebra, in naive and universal arithmetic and algebra.

That "there isn't really an ordinary inductive set", only fragments or
extensions, is that the simple naive definition of set as with regards
to its sole relation elt, that ordinary set theory like ZF which is
the usual foundation of modern mathematics, definitely has that
the inductive set of ZF, is only _properly_ logical, i.e. it's stipulated.

Subject	Author
Re: Formal Definition of Set	Ross Finlayson
Re: Formal Definition of Set	Ross Finlayson