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Canonical fragments of the strong reflection principle
Journal of Mathematical Logic ( IF 0.9 ) Pub Date : 2021-04-12 , DOI: 10.1142/s0219061321500239
Gunter Fuchs 1, 2
Affiliation  

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

中文翻译:

强反射原理的典型片段

对于任意强制类Γ, 这Γ——托多尔切维奇强反射原理的片段小号R以这样的方式被隔离: (1) 强迫公理Γ意味着Γ- 片段小号R, (2) 的固定集保留片段小号R是完整的原则小号R, 和 (3) 的子完全片段小号R暗示次完全强迫公理的主要结果。这个片段小号R和......一致CH, 甚至根据 Jensen 原理. 一路走来,一些迄今为止未知的影响(的亚完整片段)小号R对相互平稳性进行了探讨,并在一定程度上限制了小号R可能会捕捉到它们相应的强迫公理的影响。
更新日期:2021-04-12
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