Inter-universal geometry と ABC予想 (応援スレ) 44

Inter-universal geometry と ABC予想 (応援スレ) 44at MATH

Inter-universal geometry と ABC予想 (応援スレ) 44 - 暇つぶし2ch339:. Recall that a (Grothendieck) universe V is a set satisfying the following axioms [cf.[McLn], p. 194]: The various ZFC-models that we work with may be thought of as [but are not restricted to be!] the ZFC-models determined by various universes that are sets relative to some ambient ZFC-model which, in addition to the standard axioms of ZFC set theory, satisfies the following existence axiom [attributed to the “Grothendieck school” ー cf. the discussion of [McLn], p. 193]: (†G) Given any set x, there exists a universe V such that x ∈ V . We shall refer to a ZFC-model that also satisfies this additional axiom of the Grothendieck school as a ZFCG-model. This existence axiom (†G) implies, in particular, that: Given a set I and a collection of universes Vi, where i ∈ I, indexed by I [i.e., a ‘function’ I ∋ i → Vi], there exists a [larger] universe V such that Vi ∈ V , for i ∈ I. つづく

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