Inter-universal geometry と ABC予想 (応援スレ) 60at MATH
Inter-universal geometry と ABC予想 (応援スレ) 60
- 暇つぶし2ch616:α, ∈, U ∩ Vα) is only required to be 'elementary' with respect to a finite set of formulas. Ultimately, the reason for this weakening is that whereas the model-theoretic satisfaction relation ｜＝ can be defined, truth itself cannot, due to Tarski's theorem. Secondly, under ZFC it can be shown that κ is inaccessible if and only if (Vκ, ∈) is a model of second order ZFC. In this case, by the reflection property above, there exists α < κ such that (Vα, ∈) is a standard model of (first order) ZFC. Hence, the existence of an inaccessible cardinal is a stronger hypothesis than the existence of a standard model of ZFC. つづく
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