Lampoon 发表于 2025-3-21 16:42:40

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Dawdle 发表于 2025-3-21 20:13:29

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检查 发表于 2025-3-22 03:26:18

Boolean-Valued Structures,ruth values “truth” and “falsehood” by any complete Boolean algebra B. While some of the basic definitions and theorems can be generalized to the B-valued case almost mechanically the intuitive ideas behind these general notions are more difficult to perceive.

Forage饲料 发表于 2025-3-22 07:06:58

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佛刊 发表于 2025-3-22 09:50:56

Boolean-Valued Relative Constructibility,will denote the language of the first-order predicate calculus with predicate constants = and ϵ. In addition L is a first order language that is an extension of L.. In most applications L will have only finitely many constants but it may have infinitely many. M and M’ will be two B-valued structures

镇痛剂 发表于 2025-3-22 15:04:24

Forcing,hroughout this section, . denotes a standard transitive model of ., . ∈ . is a partial order structure, and . is the corresponding .-complete Boolean algebra of regular open sets of . in the relative sense of .. Further-more we have.Such that ., ., and . are related to each as described in §2. Thus

NAV 发表于 2025-3-22 19:10:13

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Fallibility 发表于 2025-3-22 23:37:30

Cardinals in V(B),ollary 14.23. However, since this translation requires the existence of elementary subsystems of . and thus cannot be carried out in . we shall try to give direct proofs in .. Corresponding to the fact that every cardinal in .[.], where 〈., .〉 is a setting for forcing and . is .-generic over ., is a

GRIEF 发表于 2025-3-23 02:58:50

Axiomatic Set Theory978-1-4684-8751-0Series ISSN 0072-5285 Series E-ISSN 2197-5612

LARK 发表于 2025-3-23 06:43:40

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查看完整版本: Titlebook: Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 1973 Springer-Verlag New York Inc. 1973 forcing.proof.set theory