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A ${\rm{\Sigma }}_4^1 $ WELLORDER OF THE REALS WITH ${\rm{NS}}_{\omega _1 } $ SATURATED

Published online by Cambridge University Press:  16 July 2019

SY-DAVID FRIEDMAN  and
STEFAN HOFFELNER
SY-DAVID FRIEDMAN
Affiliation:
KURT GÖDEL RESEARCH CENTER UNIVERSITÄT WIEN WIEN, AUSTRIA E-mail: [email protected]
STEFAN HOFFELNER
Affiliation:
WESTFÄLISCHE WILHELMS-UNIVERSITÄT MÜNSTER MÜNSTER, GERMANY E-mail: [email protected]
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Abstract

We show that, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $ , there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

Keywords

03E3503E4503E4703E55nonstationary idealprojective wellorderssaturation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1466 - 1483
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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