强反射原理的规范片段

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2020-09-13 DOI:10.1142/S0219061321500239

G. Fuchs

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引用次数: 4

摘要

对于任意强迫类[公式:见文]，todor evevic强反射原理SRP的[公式:见文]片段以这样的方式被孤立:(1)[公式:见文]的强迫公理暗示[公式:见文]的SRP片段，(2)SRP的平稳集保持片段是完整原则SRP， (3) SRP的次完备片段暗示次完备强迫公理的主要结果。这段SRP与CH，甚至与Jensen原理一致[公式:见文]。在此过程中，探索了SRP(亚完全片段)对相互平稳性的一些迄今未知的影响，并建立了SRP片段可能捕获其相应强迫公理影响的程度的一些限制。

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Canonical fragments of the strong reflection principle

For an arbitrary forcing class [Formula: see text], the [Formula: see text]-fragment of Todorčević’s strong reflection principle SRP is isolated in such a way that (1) the forcing axiom for [Formula: see text] implies the [Formula: see text]-fragment of SRP , (2) the stationary set preserving fragment of SRP is the full principle SRP , and (3) the subcomplete fragment of SRP implies the major consequences of the subcomplete forcing axiom. This fragment of SRP is consistent with CH , and even with Jensen’s principle [Formula: see text]. Along the way, some hitherto unknown effects of (the subcomplete fragment of) SRP on mutual stationarity are explored, and some limitations to the extent to which fragments of SRP may capture the effects of their corresponding forcing axioms are established.

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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.