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Transactions of the American Mathematical Society

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The calculus of partition sequences,
changing cofinalities, and
a question of Woodin


Authors: Arthur W. Apter, James M. Henle and Stephen C. Jackson
Journal: Trans. Amer. Math. Soc. 352 (2000), 969-1003
MSC (1991): Primary 03E15, 03E35, 03E60
DOI: https://doi.org/10.1090/S0002-9947-99-02554-4
Published electronically: October 15, 1999
MathSciNet review: 1695015
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Abstract | References | Similar Articles | Additional Information

Abstract: We study in this paper polarized infinite exponent partition relations. We apply our results to constructing a model for the theory ``ZF$+$DC$+\omega _1$ is the only regular, uncountable cardinal $\le\omega _{\omega _1+1}$.'' This gives a partial answer to a question of Woodin.


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Additional Information

Arthur W. Apter
Affiliation: Department of Mathematics, Baruch College, New York, New York 10010
Email: awabb@cunyvm.cuny.edu

James M. Henle
Affiliation: Department of Mathematics, Smith College, Northampton, Massachusetts 01060-2165
Email: jhenle@smith.edu

Stephen C. Jackson
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: jackson@jove.acs.unt.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02554-4
Received by editor(s): September 30, 1997
Published electronically: October 15, 1999
Additional Notes: The first author’s research was partially supported by PSC–CUNY grant 665337
Article copyright: © Copyright 1999 American Mathematical Society

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