On density of old sets in Prikry type extensions

Moti Gitik*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Every set of ordinals of cardinality κ in a Prikry extension with a measure over κ contains an old set of arbitrarily large cardinality below κ, 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 (κ, 2κ] remain. Here we would like to address this type of question.

Original languageEnglish
Pages (from-to)881-887
Number of pages7
JournalProceedings of the American Mathematical Society
Volume145
Issue number2
DOIs
StatePublished - 2017

Funding

FundersFunder number
Israel Science Foundation58/14

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