Quotients of Strongly Proper Forcings and Guessing Models

Sean Cox; John Krueger

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arXiv · 1406.3306

Quotients of Strongly Proper Forcings and Guessing Models

Sean Cox·John Krueger

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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 simple universal strongly generic conditions on a stationary set of models by certain nice regular suborders satisfy the $\omega_1$-approximation property. We prove that the existence of stationarily many $\omega_1$-guessing models in $P_{\omega_2}(H(\theta))$, for sufficiently large cardinals $\theta$, is consistent with the continuum being arbitrarily large, solving a problem of Viale and Weiss.

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BibTeX RIS

Sean Cox, John Krueger. 2014-06-12. Quotients of Strongly Proper Forcings and Guessing Models. https://arxiv.org/abs/1406.3306

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