Inter-universal geometry と ABC予想 (応援スレ) 73

Inter-universal geometry と ABC予想 (応援スレ) 73 (802ﾚｽ)
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438: １３２人目の素数さん [] 2025/08/09(土) 23:45:48.94 ID:bw4CRSHc

>>423 追加

・数学宇宙で、有名どころが3つ
　Constructible universe L
　Von Neumann universe V
Grothendieck universe U
・包含関係 L⊂V⊂U があります
　ここで、Grothendieck universe U を
　望月先生は、ZFCGなどと表現します

https://en.wikipedia.org/wiki/Von_Neumann_universe
Von Neumann universe
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC. The concept is named after John von Neumann, although it was first published by Ernst Zermelo in 1930.

https://en.wikipedia.org/wiki/Constructible_universe
Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by
L, is a particular class of sets that can be described entirely in terms of simpler sets.
L is the union of the constructible hierarchy Lα.
It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis".[1] In this paper, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent.

https://en.wikipedia.org/wiki/Grothendieck_universe
In mathematics, a Grothendieck universe is a set U with the following properties:
略
The existence of a nontrivial Grothendieck universe goes beyond the usual axioms of Zermelo–Fraenkel set theory; in particular it would imply the existence of strongly inaccessible cardinals. Tarski–Grothendieck set theory is an axiomatic treatment of set theory, used in some automatic proof systems, in which every set belongs to a Grothendieck universe. The concept of a Grothendieck universe can also be defined in a topos.[1]

http://rio2016.5ch.net/test/read.cgi/math/1753000052/438

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