Level by Level Inequivalence, Strong Compactness, and GCH

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba60-3-1

• Języki publikacji: EN

Abstrakty

EN

We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; level by level inequivalence between strong; compactness and supercompactness; non-reflecting stationary set of ordinals; Easton function; Magidor iteration of Prikry forcing

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 3
• Strony: 201--209
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Apter A. W.

• Department of Mathematics Baruch College of CUNY New York, NY 10010, U.S.A.
• The CUNY Graduate Center, Mathematics 365 Fifth Avenue New York, NY 10016, U.S.A

Bibliografia

• [1] A. Apter, A new proof of a theorem of Magidor, Arch. Math. Logic 39 (2000), 209–211.
• [2] A. Apter, Level by level inequivalence beyond measurability, Arch. Math. Logic 50 (2011), 707–712.
• [3] A. Apter, On level by level equivalence and inequivalence between strong compactness and supercompactness, Fund. Math. 171 (2002), 77–92.
• [4] A. Apter, Strong compactness, measurability, and the class of supercompact cardinals, Fund. Math. 167 (2001), 65–78.
• [5] A. Apter, Tallness and level by level equivalence and inequivalence, Math. Logic Quart. 56 (2010), 4–12.
• [6] A. Apter, Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence, Math. Logic Quart. 52 (2006), 457–463.
• [7] A. Apter, The least strongly compact can be the least strong and indestructible, Ann. Pure Appl. Logic 144 (2006), 33–42.
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• [9] A. Apter, V. Gitman and J. Hamkins, Inner models with large cardinal features usually obtained by forcing, Arch. Math. Logic 51 (2012), 257–283.
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