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PFA AND THE DEFINABILITY OF THE NONSTATIONARY IDEAL

Part of: Set theory

Published online by Cambridge University Press:  11 April 2025

STEFAN HOFFELNER Open the ORCID record for STEFAN HOFFELNER [Opens in a new window] ,
PAUL LARSON Open the ORCID record for PAUL LARSON [Opens in a new window] ,
RALF SCHINDLER Open the ORCID record for RALF SCHINDLER [Opens in a new window]  and
LIUZHEN WU Open the ORCID record for LIUZHEN WU [Opens in a new window]
STEFAN HOFFELNER
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UNIVERSITÄT MÜNSTER EINSTEINSTR. 62, MÜNSTER GERMANY E-mail: stefan.hoffelner@gmx.at E-mail: rds@uni-muenster.de
PAUL LARSON*
Affiliation:
DEPARTMENT OF MATHEMATICS MIAMI UNIVERSITY OXFORD, OHIO 45056
RALF SCHINDLER
Affiliation:
INSTITUT FÜR MATHEMATISCHE LOGIK UNIVERSITÄT MÜNSTER EINSTEINSTR. 62, MÜNSTER GERMANY E-mail: stefan.hoffelner@gmx.at E-mail: rds@uni-muenster.de
LIUZHEN WU
Affiliation:
INSTITUTE OF MATHEMATICS ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE CHINESE ACADEMY OF SCIENCES BEIJING 100190 CHINA and SCHOOL OF MATHEMATICAL SCIENCES UNIVERSITY OF CHINESE ACADEMY OF SCIENCES BEIJING 100049 CHINA E-mail: lzwu@math.ac.cn
*
E-mail: larsonpb@miamioh.edu
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Abstract

We produce, relative to a $\textsf {ZFC}$ model with a supercompact cardinal, a $\textsf {ZFC}$ model of the Proper Forcing Axiom in which the nonstationary ideal on $\omega _1$ is $\Pi _1$-definable in a parameter from $H_{\aleph _2}$.

Keywords

proper forcing axiomnonstationary idealforcingcountable support iteration

MSC classification

Primary: 03E35: Consistency and independence results 03E47: Other notions of set-theoretic definability

Information

Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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