Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-19T22:37:33.316Z Has data issue: false hasContentIssue false
  • English
  • Français

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/
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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[As2] Asperó, David, Coding into H(κ+) without parameters, unpublished note, 2006.Google Scholar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