The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2
Dima Sinapova
Source: J. Symbolic Logic Volume 77, Issue 3
(2012), 934-946.
Abstract
We show that given ω many supercompact cardinals, there is a generic extension in which the tree property holds at ℵω2+1 and the SCH fails at ℵω2.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1344862168
Digital Object Identifier: doi:10.2178/jsl/1344862168
Mathematical Reviews number (MathSciNet): MR2987144
References
James Baumgartner, Matthew Foreman, and Otmar Spinas The spectrum of the $\Gamma$-invariant of a bilinear space, Journal of Algebra, vol. 189(1997), no. 2, pp. 406–418.
Mathematical Reviews (MathSciNet): MR1438183
Zentralblatt MATH: 0869.03030
Digital Object Identifier: doi:10.1006/jabr.1996.6852
James Cummings and Matthew Foreman Diagonal Prikry extensions, Journal of Symbolic Logic, vol. 75(2010), no. 4, pp. 1383–1402.
Mathematical Reviews (MathSciNet): MR2767975
Zentralblatt MATH: 05835172
Digital Object Identifier: doi:10.2178/jsl/1286198153
Project Euclid: euclid.jsl/1286198153
James Cummings, Matthew Foreman, and Menachem Magidor Squares, scales and stationary reflection, Journal of Mathematical Logic, vol. 1(2001), pp. 35–98.
Mathematical Reviews (MathSciNet): MR1838355
Zentralblatt MATH: 0988.03075
Digital Object Identifier: doi:10.1142/S021906130100003X
–––– Canonical structure in the universe of set theory I, Annals of Pure and Applied Logic, vol. 129(2004), no. 1–3, pp. 211–243.
Mathematical Reviews (MathSciNet): MR2078366
Zentralblatt MATH: 1058.03051
Digital Object Identifier: doi:10.1016/j.apal.2004.04.002
–––– Canonical structure in the universe of set theory II, Annals of Pure and Applied Logic, vol. 142(2006), no. 1–3, pp. 55–75.
Mathematical Reviews (MathSciNet): MR2250537
Zentralblatt MATH: 1096.03060
Digital Object Identifier: doi:10.1016/j.apal.2005.11.007
Moti Gitik and Assaf Sharon On SCH and the approachability property, Proceedings of the American Mathematical Society, vol. 136(2008), pp. 311–320.
Mathematical Reviews (MathSciNet): MR2350418
Zentralblatt MATH: 1140.03033
Digital Object Identifier: doi:10.1090/S0002-9939-07-08716-3
Thomas Jech Set theory, Springer Monographs in Mathematics, Springer-Verlag,2003.
Mathematical Reviews (MathSciNet): MR1940513
Menachem Magidor Reflecting stationary sets, Journal of Symbolic Logic, vol. 47(1982), no. 4, pp. 755–771.
Mathematical Reviews (MathSciNet): MR683153
Zentralblatt MATH: 0506.03014
Digital Object Identifier: doi:10.2307/2273097
Menachem Magidor and Saharon Shelah The tree property at successors of singular cardinals, Archive for Mathematical Logic, vol. 35(1996), no. 5–6, pp. 385–404.
Mathematical Reviews (MathSciNet): MR1420265
Zentralblatt MATH: 0874.03060
Digital Object Identifier: doi:10.1007/s001530050052
Itay Neeman Aronszajn trees and the failure of the singular cardinal hypothesis, Journal of Mathematical Logic, vol. 9(2009), pp. 139–157.
Mathematical Reviews (MathSciNet): MR2665784
Zentralblatt MATH: 1204.03050
Digital Object Identifier: doi:10.1142/S021906130900080X
Saharon Shelah Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press,1994.
Mathematical Reviews (MathSciNet): MR1318912
Robert M. Solovay Strongly compact cardinals and the GCH, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Univ. California, Berkeley, Calif., 1971), American Mathematical Society,1974, pp. 365–372.
Mathematical Reviews (MathSciNet): MR379200
Zentralblatt MATH: 0317.02083
Spencer Unger preprint.
