不相容有界范畴强迫公理

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2021-01-08 DOI:10.1142/s0219061322500064

D. Asperó, M. Viale

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引用次数: 4

摘要

我们为表现良好的类引入有界范畴强制公理[公式:见文本]。这些是有界强迫公理的强大形式，它们完全决定了宇宙某些初始部分的理论[公式:见文]中的模强迫，对于一些基数[公式:见文]自然地与[公式:见文]相关联。这些公理自然地将任意集合强制的射影绝对性——在这种情况下[公式:见文]——扩展到具有[公式:见文]的类[公式:见文]。与射影绝对性不同，这些高有界范畴强制公理不遵循大基数公理，但可以在温和的大基数假设下强制[公式:见文本]。我们还证明了许多类的存在[公式:见文]，而[公式:见文]产生了[公式:见文]的成对不相容理论。

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Incompatible bounded category forcing axioms

We introduce bounded category forcing axioms for well-behaved classes [Formula: see text]. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe [Formula: see text] modulo forcing in [Formula: see text], for some cardinal [Formula: see text] naturally associated to [Formula: see text]. These axioms naturally extend projective absoluteness for arbitrary set-forcing — in this situation [Formula: see text] — to classes [Formula: see text] with [Formula: see text]. Unlike projective absoluteness, these higher bounded category forcing axioms do not follow from large cardinal axioms but can be forced under mild large cardinal assumptions on [Formula: see text]. We also show the existence of many classes [Formula: see text] with [Formula: see text] giving rise to pairwise incompatible theories for [Formula: see text].

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来源期刊

Journal of Mathematical Logic MATHEMATICS-LOGIC

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.