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QUOTIENTS OF STRONGLY PROPER FORCINGS AND GUESSING MODELS

Published online by Cambridge University Press:  09 March 2016

SEAN COX  and
JOHN KRUEGER
SEAN COX
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VIRGINIA COMMONWEALTH UNIVERSITY 1015 FLOYD AVENUE PO BOX 842014 RICHMOND, VIRGINIA 23284, USAE-mail: scox9@vcu.edu
JOHN KRUEGER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS 1155 UNION CIRCLE #311430 DENTON, TX 76203, USAE-mail: jkrueger@unt.edu
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Abstract

We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have universal strongly generic conditions on a stationary set of models by certain nice regular suborders satisfy the ω1-approximation property. We prove that the existence of stationarily many ω1-guessing models in Pω2(H(θ)), for sufficiently large cardinals θ, is consistent with the continuum being arbitrarily large, solving a problem of Viale and Weiss [13].

Keywords

Primary 03E40Secondary 03E35strongly properapproximation propertyadequate set forcingguessing model
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 264 - 283
Copyright
Copyright © The Association for Symbolic Logic 2016 

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