不安 发表于 2025-3-30 11:56:25

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教义 发表于 2025-3-30 13:46:02

The Fundamental Operations,tially as the union of a sequence of sets .., . ∈ On which were so defined that . ∈ .. iff there exists a wff .(.., .., ..., ..) having no free variables other than .., .., ... , .. and there exist .. , ..., .. ∈ .. such that ..

显示 发表于 2025-3-30 20:03:43

The Arithmetization of Model Theory,a standard model of ZF means in particular that ? is a model of Axiom 5, the Axiom Schema of Replacement. Since Axiom 5 is a schema “M is a standard model of ZF” is a meta-statement asserting that a certain infinite collection of sentences of ZF hold. Can this metastatement be formalized in ZF, that

我邪恶 发表于 2025-3-30 21:36:08

Forcing,h a predicate will be defined in this section. When this predicate holds we say that < {.., ..., ..}, {.., ..., ..}> forces ⌜.⌝. The ordered pair <{.., ..., ..}, {.., ..., ..}> is called a forcing condition.

先兆 发表于 2025-3-31 04:18:06

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indoctrinate 发表于 2025-3-31 05:54:53

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Glutinous 发表于 2025-3-31 10:36:22

Gaisi Takeuti,Wilson M. Zaringics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are prov

谄媚于性 发表于 2025-3-31 15:23:15

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变化无常 发表于 2025-3-31 19:27:00

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Feigned 发表于 2025-4-1 01:10:11

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查看完整版本: Titlebook: Introduction to Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 19711st edition Springer-Verlag Berlin Heidelberg 1971 arith