Fusion and large cardinal preservation |
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Authors: | Sy-David Friedman Radek Honzik Lyubomyr Zdomskyy |
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Affiliation: | 1. Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Wien, Austria;2. Charles University, Department of Logic, Celetná 20, Praha 1, 116 42, Czech Republic |
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Abstract: | In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size ?κ not only does not collapse κ+ but also preserves the strength of κ (after a suitable preparatory forcing). This provides a general theory covering the known cases of tree iterations which preserve large cardinals (cf. Dobrinen and Friedman (2010) [3], Friedman and Halilovi? (2011) [5], Friedman and Honzik (2008) [6], Friedman and Magidor (2009) [8], Friedman and Zdomskyy (2010) [10], Honzik (2010) [12]). |
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Keywords: | primary, 03E55, 03E35 secondary, 03E40, 03E17 |
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