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Coding the Universe

Journal of Symbolic Logic 50 (4):1081-1081 (1985)

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  1. Chains of end elementary extensions of models of set theory.Andres Villaveces - 1998 - Journal of Symbolic Logic 63 (3):1116-1136.
    Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained in this fashion (`unfoldable cardinals') lie in the boundary of the propositions consistent with `V = L' and the existence of 0 ♯ . We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various forcing constructions.
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  • A combinatorial forcing for coding the universe by a real when there are no sharps.Saharon Shelah & Lee J. Stanley - 1995 - Journal of Symbolic Logic 60 (1):1-35.
    Assuming 0 ♯ does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct appeal to fine structure itself.
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  • A guide to "coding the universe" by Beller, Jensen, Welch.Sy D. Friedman - 1985 - Journal of Symbolic Logic 50 (4):1002-1019.
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  • The Transfinite Universe.W. Hugh Woodin - 2011 - In Matthias Baaz (ed.), Kurt Gödel and the foundations of mathematics: horizons of truth. New York: Cambridge University Press. pp. 449.
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  • Results on the Generic Kurepa Hypothesis.R. B. Jensen & K. Schlechta - 1990 - Archive for Mathematical Logic 30 (1):13-27.
    K.J. Devlin has extended Jensen's construction of a model ofZFC andCH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees inccc-generic extensions. We use a partially defined ◊-sequence, given by a fine structure lemma. We also show that the usual collapse ofκ Mahlo toω 2 will give a model without Kurepa trees not only in the model itself, but also inccc-extensions.
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