Tree forcings and sharps

Fabiana Castiblanco,

Fabiana Castiblanco

[email protected]

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

Search for more papers by this author

Philipp Schlicht,

Corresponding Author

Philipp Schlicht

[email protected]

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, GermanySearch for more papers by this author

Fabiana Castiblanco,

Fabiana Castiblanco

[email protected]

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

Search for more papers by this author

Philipp Schlicht,

Corresponding Author

Philipp Schlicht

[email protected]

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, GermanySearch for more papers by this author

First published: 25 October 2016

https://doi.org/10.1002/pamm.201610443

About

PDF

Tools

Share a link

Email
Wechat
Bluesky

Abstract

The Levy-Solovay theorem and its variants show that various large cardinals are preserved under small forcings. We study the preservation of consequences of large cardinals under proper forcings. In particular, we consider the preservation of the statement that every real has a sharp for classical tree forcings. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

References

[1] T. Jech, Set theory, Springer Monographs in Mathematics (Springer-Verlag, Berlin, 2003), The third millennium edition, revised and expanded.
Google Scholar
[2] J. D. Hamkins and W. H. Woodin, Proc. Amer. Math. Soc. 128(10), 3025–3029 (2000).
Google Scholar
[3] D. A. Martin and R. M. Solovay, Ann. of Math. (2) 89, 138–159 (1969).
Google Scholar
[4] L. J. Halbeisen, Combinatorial set theory, Springer Monographs in Mathematics (Springer, London, 2012), With a gentle introduction to forcing.
Google Scholar
[5] D. Ikegami, Ann. Pure Appl. Logic 161(7), 879–894 (2010).
Google Scholar
[6] L. Harrington, J. Symbolic Logic 43(4), 685–693 (1978).
Google Scholar
[7] D. A. Martin, Fund. Math. 66, 287–291 (1969/1970).
Google Scholar
[8] F. Castiblanco and P. Schlicht, Tree forcings, sharps and thin equivalence relations, in preparation.
Google Scholar
[9] P. Schlicht, Ann. Pure Appl. Logic 165(10), 1577–1625 (2014).
Google Scholar
[10] J. R. Steel, An outline of inner model theory, in: Handbook of set theory. Vols. 1, 2, 3, (Springer, Dordrecht, 2010), pp. 1595–1684.
Google Scholar
[11] W. J. Mitchell and J. R. Steel, Fine structure and iteration trees, Lecture Notes in Logic, Vol. 3 (Springer-Verlag, Berlin, 1994).
Google Scholar
[12] J. R. Steel, J. Symbolic Logic 67(3), 1197–1226 (2002).
Google Scholar
[13] M. Foreman and M. Magidor, Ann. Pure Appl. Logic 76(1), 47–97 (1995).
Google Scholar