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An elementary approach to the fine structure of L

Sy D. Friedman & Peter Koepke

Bulletin of Symbolic Logic 3 (4):453-468 (1997)

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Set forcing and strong condensation for H.Liuzhen Wu - 2015 - Journal of Symbolic Logic 80 (1):56-84.details The Axiom of Strong Condensation, first introduced by Woodin in [14], is an abstract version of the Condensation Lemma ofL. In this paper, we construct a set-sized forcing to obtain Strong Condensation forH. As an application, we show that “ZFC + Axiom of Strong Condensation +”is consistent, which answers a question in [14]. As another application, we give a partial answer to a question of Jech by proving that “ZFC + there is a supercompact cardinal + any ideal onω1which is (...) Download Export citation Bookmark
1998 European Summer Meeting of the Association for Symbolic Logic.S. Buss - 1999 - Bulletin of Symbolic Logic 5 (1):59-153.details Download Export citation Bookmark
Global square and mutual stationarity at the ℵn.Peter Koepke & Philip D. Welch - 2011 - Annals of Pure and Applied Logic 162 (10):787-806.details We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...) Download Export citation Bookmark
Hyperfine Structure Theory and Gap 1 Morasses.Sy-David Friedman, Peter Koepke & Boris Piwinger - 2006 - Journal of Symbolic Logic 71 (2):480 - 490.details Using the Friedman-Koepke Hyperfine Structure Theory of [2], we provide a short construction of a gap 1 morass in the constructible universe. Download Export citation Bookmark 1 citation
Square below a non-weakly compact cardinal.Hazel Brickhill - 2020 - Archive for Mathematical Logic 59 (3-4):409-426.details In his seminal paper introducing the fine structure of L, Jensen proved that under \ any regular cardinal that reflects stationary sets is weakly compact. In this paper we give a new proof of Jensen’s result that is straight-forward and accessible to those without a knowledge of Jensen’s fine structure theory. The proof here instead uses hyperfine structure, a very natural and simpler alternative to fine structure theory introduced by Friedman and Koepke. Download Export citation Bookmark

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