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Axiom I 0 and higher degree theory

Journal of Symbolic Logic 80 (3):970-1021 (2015)

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Incomparable Vγ$V_\gamma$‐degrees.Teng Zhang - 2023 - Mathematical Logic Quarterly 69 (1):58-62.details In [3], Shi proved that there exist incomparable Zermelo degrees at γ if there exists an ω‐sequence of measurable cardinals, whose limit is γ. He asked whether there is a size antichain of Zermelo degrees. We consider this question for the ‐degree structure. We use a kind of Prikry‐type forcing to show that if there is an ω‐sequence of measurable cardinals, then there are ‐many pairwise incomparable ‐degrees, where γ is the limit of the ω‐sequence of measurable cardinals. Download Export citation Bookmark
Generic at.Vincenzo Dimonte - 2018 - Mathematical Logic Quarterly 64 (1-2):118-132.details In this paper we introduce a generic large cardinal akin to, together with the consequences of being such a generic large cardinal. In this case is Jónsson, and in a choiceless inner model many properties hold that are in contrast with pcf theory in. Download Export citation Bookmark
$$I_0$$ and combinatorics at $$\lambda ^+$$.Nam Trang & Xianghui Shi - 2017 - Archive for Mathematical Logic 56 (1):131-154.details We investigate the compatibility of $$I_0$$ with various combinatorial principles at $$\lambda ^+$$, which include the existence of $$\lambda ^+$$ -Aronszajn trees, square principles at $$\lambda $$, the existence of good scales at $$\lambda $$, stationary reflections for subsets of $$\lambda ^{+}$$, diamond principles at $$\lambda $$ and the singular cardinal hypothesis at $$\lambda $$. We also discuss whether these principles can hold in $$L(V_{\lambda +1})$$. Download Export citation Bookmark 2 citations

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