On SCH and the approachability property
HTML articles powered by AMS MathViewer
- by Moti Gitik and Assaf Sharon PDF
- Proc. Amer. Math. Soc. 136 (2008), 311-320 Request permission
Abstract:
We construct a model of ${}^\neg SCH +^\neg AP +$ (Very Good Scale). This answers questions of Cummings, Foreman, Magidor and Woodin.References
- Shai Ben-David and Menachem Magidor, The weak $\square ^\ast$ is really weaker than the full $\square$, J. Symbolic Logic 51 (1986), no. 4, 1029–1033. MR 865928, DOI 10.2307/2273914
- James Cummings, Matthew Foreman, and Menachem Magidor, Squares, scales and stationary reflection, J. Math. Log. 1 (2001), no. 1, 35–98. MR 1838355, DOI 10.1142/S021906130100003X
- James Cummings and Ernest Schimmerling, Indexed squares, Israel J. Math. 131 (2002), 61–99. MR 1942302, DOI 10.1007/BF02785851
- Moti Gitik and Menachem Magidor, Extender based forcings, J. Symbolic Logic 59 (1994), no. 2, 445–460. MR 1276624, DOI 10.2307/2275399
- M. Gitik, Prikry Type Forcings, Handbook of Set Theory, eds. M. Foreman, A. Kanamori and M. Magidor,to appear. (www.math.tau.ac.il/ gitik)
- Thomas Jech, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. The third millennium edition, revised and expanded. MR 1940513
- Akihiro Kanamori, The higher infinite, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1994. Large cardinals in set theory from their beginnings. MR 1321144
- C. Merimovich, A Power Function with a Fixed Finite Gap Everywhere, J. of Symbolic Logic, to appear (arXiv:math.LO/0005179).
- Saharon Shelah, On successors of singular cardinals, Logic Colloquium ’78 (Mons, 1978) Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam-New York, 1979, pp. 357–380. MR 567680
- Saharon Shelah, Reflecting stationary sets and successors of singular cardinals, Arch. Math. Logic 31 (1991), no. 1, 25–53. MR 1126352, DOI 10.1007/BF01370693
- Saharon Shelah, Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1318912
- Robert M. Solovay, Strongly compact cardinals and the GCH, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 365–372. MR 0379200
Additional Information
- Moti Gitik
- Affiliation: School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
- MR Author ID: 74045
- Email: gitik@post.tau.ac.il
- Assaf Sharon
- Affiliation: School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
- Address at time of publication: Department of Mathematics, University of California, Irvine, California 92717
- Email: sharona@math.uci.edu
- Received by editor(s): April 17, 2005
- Received by editor(s) in revised form: December 5, 2005, and March 14, 2006
- Published electronically: October 12, 2007
- Additional Notes: The authors are grateful to John Krueger, James Cummings and the referee for their remarks and corrections
- Communicated by: Julia Knight
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 311-320
- MSC (2000): Primary 03E35, 03E55
- DOI: https://doi.org/10.1090/S0002-9939-07-08716-3
- MathSciNet review: 2350418