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Quotients of Strongly Proper Forcings and Guessing Models
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 -approximation
property. We prove that the existence of stationarily many -guessing
models in , for sufficiently large cardinals ,
is consistent with the continuum being arbitrarily large, solving a problem of
Viale and Weiss
Cynthia L. Horn, Plaintiff, v. Knight Facilities Management -- GM, Inc., a Delaware corporation, Defendant.
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