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Definable well-orders of H(ω2) and GCH

Published online by Cambridge University Press:  12 March 2014

David Asperó  and
Sy-David Friedman
David Asperó
Affiliation:
Institute of Discrete Mathematics and Geometry, Technische Universität Wien, Wiedner Hauptstraße 8–10/104, A-1040 Wien, Austria, E-mail: [email protected]
Sy-David Friedman
Affiliation:
Kurt Gödel Research Center, Universität Wien, Währinger Straße 25, A-1090 Wien, Austria, E-mail: [email protected], URL: http://www.logic.univie.ac.at/~sdf/
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Abstract

Assuming 2ℵ0 = ℵ1 and 2ℵ1 = ℵ2, we build a partial order that forces the existence of a well-order of H(ω2) lightface definable over ⟨H(ω1), ∈⟩ and that preserves cardinal exponentiation and cofinalities.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1101 - 1121
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[A-S] Abraham, Uri and Shelah, Saharon, Coding with ladders a well ordering of the reals, this Journal, vol. 67 (2002), pp. 579–597.Google Scholar
[As1] Asperó, David, Coding by club-sequences, Annals of Pure and Applied Logic, vol. 142 (2006), pp. 98–114.CrossRefGoogle Scholar
[As2] Asperó, David, Coding into H(κ+) without parameters, unpublished note, 2006.Google Scholar
[As3] Asperó, David, Coding into H(ω2), together (or not) with forcing axioms. A survey, Computational prospects of infinity, Part II: Presented talks, IMS Lecture Notes, vol. 15, Natl. Univ. Singapore, 2008.Google Scholar
[As-F] Asperó, David and Friedman, Sy-David, Large cardinals and locally defined well-orders of the universe, Annals of Pure and Applied Logic, vol. 157 (2009), pp. 1–15.CrossRefGoogle Scholar
[B] Brooke-Taylor, Andrew, Large cardinals and definable well-orderings of the universe, this Journal, vol. 74 (2009), pp. 641–654.Google Scholar
[F] Friedman, Sy-David, Forcing condensation, notes, 2008.Google Scholar
[FH] Friedman, Sy-David and Holy, Peter, Condensation and large cardinals, Fundamenta Mathematicae, vol. 215 (2011), no. 2, pp. 133–166.CrossRefGoogle Scholar
[J] Jech, Thomas, Set theory, Springer, 2002.Google Scholar
[M] Moore, Justin T., Set mapping reflection, Journal of Mathematical Logic, vol. 5 (2005), no. 1, pp. 87–98.CrossRefGoogle Scholar