The Wholeness Axioms and the Class of Supercompact Cardinals

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba60-2-1

• Języki publikacji: EN

Abstrakty

EN

We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.

Słowa kluczowe

EN

Wholeness Axioms; supercompact cardinal; strongly compact cardinal; indestructibility; level by level equivalence between strong compactness and supercompactness; non-reflecting stationary set of ordinals

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 2
• Strony: 101--111
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Apter A. W.

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

Bibliografia

• [1] A. W. Apter, Laver indestructibility and the class of compact cardinals, J. Symbolic Logic 63 (1998), 149–157.
• [2] -, Some remarks on indestructibility and Hamkins’ lottery preparation, Arch. Math. Logic 42 (2003), 717–735.
• [3] -, Some structural results concerning supercompact cardinals, J. Symbolic Logic 66 (2001), 1919–1927.
• [4] A. W. Apter and Sh. Friedman, Coding into HOD via normal measures with some applications, Math. Logic Quart. 57 (2011), 366–372.
• [5] A. W. Apter and S. Shelah, On the strong equality between supercompactness and strong sompactness, Trans. Amer. Math. Soc. 349 (1997), 103–128.
• [6] P. Corazza, Consistency of V = HOD with the Wholeness Axiom, Arch. Math. Logic 39 (2000), 219–226.
• [7] -, Lifting elementary embeddings j : Vλ→Vλ, ibid. 46 (2007), 61–72.
• [8] -, The gap between I3 and the Wholeness Axiom, Fund. Math. 179 (2003), 43–60.
• [9] P. Corazza, The spectrum of elementary embeddings j : V ! V , Ann. Pure Appl. Logic 139 (2006), 327–399.
• [10] -, The Wholeness Axiom and Laver sequences, ibid. 105 (2000), 157–260.
• [11] J. D. Hamkins, The lottery preparation, ibid. 101 (2000), 103–146.
• [12] -, The Wholeness Axioms and V = HOD, Arch. Math. Logic 40 (2001), 1–8.
• [13] T. Jech, Set Theory. The Third Millennium Edition, Revised and Expanded, Springer, Berlin, 2003.
• [14] A. Kanamori, The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, 2nd ed., Springer, Berlin, 2003.
• [15] Y. Kimchi and M. Magidor, The independence between the concepts of compactness and supercompactness, circulated manuscript.
• [16] K. Kunen, Elementary embeddings and infinitary combinatorics, J. Symbolic Logic 36 (1971), 407–413.
• [17] R. Laver, Making the supercompactness of k- indestructible under k-directed closed forcing, Israel J. Math. 29 (1978), 385–388.
• [18] T. K. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1974/75), 327–359.