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On density of old sets in Prikry type extensions


Author: Moti Gitik
Journal: Proc. Amer. Math. Soc. 145 (2017), 881-887
MSC (2010): Primary 03E35; Secondary 03E55
DOI: https://doi.org/10.1090/proc/13312
Published electronically: August 23, 2016
MathSciNet review: 3577887
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Abstract: Every set of ordinals of cardinality $ \kappa $ in a Prikry extension with a measure over $ \kappa $ contains an old set of arbitrarily large cardinality below $ \kappa $, and, actually, it can be split into countably many old sets. What about sets with larger cardinalities? Clearly, any set of ordinals in a forcing extension of a regular cardinality above the cardinality of the forcing used, contains an old set of the same cardinality. Still cardinals in the interval $ (\kappa , 2^\kappa ]$ remain. Here we would like to address this type of question.


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Additional Information

Moti Gitik
Affiliation: Department of Mathematics, Tel Aviv University, Tel Aviv, Israel.

DOI: https://doi.org/10.1090/proc/13312
Received by editor(s): April 24, 2016
Published electronically: August 23, 2016
Additional Notes: This work was partially supported by ISF grant no. 58/14
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society