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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
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 S R P is isolated in such a way that (1) the forcing axiom for Γ implies the Γ -fragment of S R P , (2) the stationary set preserving fragment of S R P is the full principle S R P , and (3) the subcomplete fragment of S R P implies the major consequences of the subcomplete forcing axiom. This fragment of S R P is consistent with C H , and even with Jensen’s principle ♢ . Along the way, some hitherto unknown effects of (the subcomplete fragment of) S R P on mutual stationarity are explored, and some limitations to the extent to which fragments of S R P may 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 磷 以这样的方式被隔离: (1) 强迫公理Γ 意味着Γ - 片段小号 R 磷 , (2) 的固定集保留片段小号 R 磷 是完整的原则小号 R 磷 , 和 (3) 的子完全片段小号 R 磷 暗示次完全强迫公理的主要结果。这个片段小号 R 磷 和......一致C H , 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 磷 对相互平稳性进行了探讨,并在一定程度上限制了小号 R 磷 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
中文翻译:
强反射原理的典型片段
对于任意强制类