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On the consistency of local and global versions of Chang's Conjecture


Authors: Monroe Eskew and Yair Hayut
Journal: Trans. Amer. Math. Soc. 370 (2018), 2879-2905
MSC (2010): Primary 03EXX
DOI: https://doi.org/10.1090/tran/7260
Published electronically: November 17, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for many pairs of infinite cardinals $ \kappa > \mu ^+ > \mu $, $ (\kappa ^{+}, \kappa )\twoheadrightarrow (\mu ^+, \mu )$ is consistent relative to the consistency of a supercompact cardinal. We also show that it is consistent, relative to a huge cardinal, that $ (\kappa ^{+}, \kappa )\twoheadrightarrow (\mu ^+, \mu )$ for every successor cardinal $ \kappa $ and every $ \mu < \kappa $, answering a question of Foreman.


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Additional Information

Monroe Eskew
Affiliation: Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, P.O. Box 842014, Richmond, Virginia 23284
Address at time of publication: Kurt Gödel Research Center, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria
Email: monroe.eskew@univie.ac.at

Yair Hayut
Affiliation: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Email: yair.hayut@math.huji.ac.il

DOI: https://doi.org/10.1090/tran/7260
Received by editor(s): July 16, 2016
Received by editor(s) in revised form: July 25, 2016, and February 7, 2017
Published electronically: November 17, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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