Inter-universal geometry と ABC予想 (応援スレ) 45

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 45 (1002ﾚｽ)
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252: 2020/05/08(金)13:45 ID:qXGvfbUV(8/26) AA×
>>236

外部ﾘﾝｸ:en.wikipedia.org
外部ﾘﾝｸ:en.wikipedia.org

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252:  [sage] 2020/05/08(金) 13:45:23 ID:qXGvfbUV

>>236
>https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
>Zermelo-Fraenkel set theory
> 2.3 3. Axiom schema of specification (also called the axiom schema of separation or of restricted comprehension)
(引用終り)

追加
これ、現代では大分見直しされているようですね（＾＾；
https://en.wikipedia.org/wiki/Axiom_schema_of_specification
Axiom schema of specification
(抜粋)
In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.

Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Godel considered it the most important axiom of set theory.

Relation to the axiom schema of replacement
The axiom schema of separation can almost be derived from the axiom schema of replacement.
For this reason, the axiom schema of specification is often left out of modern lists of the Zermelo?Fraenkel axioms. However, it's still important for historical considerations, and for comparison with alternative axiomatizations of set theory, as can be seen for example in the following sections.
Unrestricted comprehension
Accepting only the axiom schema of specification was the beginning of axiomatic set theory.
Most of the other Zermelo?Fraenkel axioms (but not the axiom of extensionality, the axiom of regularity, or the axiom of choice) then became necessary to make up for some of what was lost by changing the axiom schema of comprehension to the axiom schema of specification ? each of these axioms states that a certain set exists,
and defines that set by giving a predicate for its members to satisfy, i.e. it is a special case of the axiom schema of comprehension.

http://rio2016.5ch.net/test/read.cgi/math/1588552720/252

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