TY - JOUR

T1 - On density of old sets in Prikry type extensions

AU - Gitik, Moti

N1 - Publisher Copyright:
© 2016 American Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85005951178&partnerID=8YFLogxK

U2 - 10.1090/proc/13312

DO - 10.1090/proc/13312

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AN - SCOPUS:85005951178

SN - 0002-9939

VL - 145

SP - 881

EP - 887

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -