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Approachability at the second successor of a singular cardinal

Published online by Cambridge University Press:  12 March 2014

Moti Gitik  and
John Krueger
Moti Gitik
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, E-mail: gitik@post.tau.ac.il URL: http://www.math.tau.ac.il/~gitik
John Krueger
Affiliation:
Department of Mathematics, University of California, Berkeley, Berkeley, Ca 94720, USA, E-mail: jkrueger@math.berkeley.edu URL: http://www.math.berkeley.edu/~jkrueger
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Abstract

We prove that if μ is a regular cardinal and ℙ is a μ-centered forcing poset, then ℙ forces that (I[μ++[)V generates I[μ++] modulo clubs. Using this result, we construct models in which the approachability property fails at the successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.

Keywords

approachability idealinternally approachable
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1211 - 1224
Copyright
Copyright © Association for Symbolic Logic 2009

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