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Canonical measure assignments

Published online by Cambridge University Press:  12 March 2014

Steve Jackson  and
Benedikt Löwe
Steve Jackson
Affiliation:
Department of Mathematics, University of North Texas, Denton, P.O. Box 311430, TX 76203-1430, USA, E-mail:[email protected] Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH, UK Corpus Christi College, University of Cambridge, Cambridge, CB2 1RH, UK, E-mail:[email protected]
Benedikt Löwe
Affiliation:
Institute for Logic Language and Computation, Universiteit Van Amsterdam, Postbus 94242, 1090 Ge Amsterdam, The Netherlands Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH, UK Corpus Christi College, University of Cambridge, Cambridge, CB2 1RH, UK, E-mail:[email protected]
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Abstract

We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal κ < ℵ ε0 in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 403 - 424
Copyright
Copyright © Association for Symbolic Logic 2013

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References

REFERENCES

[1]Bold, Stefan and Löwe, Benedikt, A simple inductive measure analysis for cardinals under the axiom of determinacy, Advances in logic (Gao, Su, Jackson, Steve, and Zhang, Yi, editors), Contemporary Mathematics, vol. 425, American Mathematical Society, 2007, pp. 23–41.CrossRefGoogle Scholar
[2]Grätzer, George, Universal algebra, 2nd ed., Springer-Verlag, 1968.Google Scholar
[3]Jackson, Steve, AD and the projective ordinals, Cabal seminar 81–85 (Kechris, Alexander S., Martin, Donald A., and Steel, John R., editors), Lecture Notes in Mathematics, vol. 1333, SpringerVerlag, 1988, pp. 117–220.CrossRefGoogle Scholar
[4]Jackson, Steve, A computation of , Memoirs of the American Mathematical Society, vol. 140 (1999).CrossRefGoogle Scholar
[5]Jackson, Steve, Structural consequences of AD, Handbook of set theory (Foreman, Matt, Kanamori, Akihiro, and Magidor, Menachem, editors), vol. 3, Springer-Verlag, 2010, pp. 1753–1876.CrossRefGoogle Scholar
[6]Jackson, Steve and Khafizov, Farid T., Descriptions and cardinals below , this Journal, to appear.Google Scholar
[7]Kanamori, Akihiro, The higher infinite, large cardinals in set theory from their beginnings, Perspectives in Mathematical Logic, Springer-Verlag, 1994.Google Scholar
[8]Kechris, Alexander S., AD and projective ordinals, Cabal seminar 76–77 (Kechris, Alexander S. and Moschovakis, Yiannis N., editors), Lecture Notes in Mathematics, vol. 689, Springer-Verlag, 1978, pp. 91–132.CrossRefGoogle Scholar
[9]Kleinberg, Eugene M., Infinitary combinatorics and the axiom of determinateness. Lecture Notes in Mathematics, vol. 612, Springer-Verlag, 1977.CrossRefGoogle Scholar
[10]Löwe, Benedikt, Kleinberg sequences and partition cardinals below , Fundamenta Mathematical, vol. 171 (2002), pp. 69–76.CrossRefGoogle Scholar
[11]Moschovakis, Yiannis N., Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland, 1980.Google Scholar