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NAMBA FORCING, WEAK APPROXIMATION, AND GUESSING

Published online by Cambridge University Press:  21 December 2018

SEAN COX  and
JOHN KRUEGER
SEAN COX
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VIRGINIA COMMONWEALTH UNIVERSITY 1015 FLOYD AVENUE PO BOX 842014 RICHMOND, VIRGINIA23284, USAE-mail:scox9@vcu.edu
JOHN KRUEGER
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS 1155 UNION CIRCLE #311430 DENTON, TX76203, USAE-mail:jkrueger@unt.edu
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Abstract

We prove a variation of Easton’s lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle IGMP, GMP together with 2ω ≤ ω2 is consistent with the existence of an ω1-distributive nowhere c.c.c. forcing poset of size ω1. We introduce the idea of a weakly guessing model, and prove that many of the strong consequences of the principle GMP follow from the existence of stationarily many weakly guessing models. Using Namba forcing, we construct a model in which there are stationarily many indestructibly weakly guessing models which have a bounded countable subset not covered by any countable set in the model.

Keywords

03E0503E3503E4003E65weak ω1-approximation propertyweak ω1-guessingwGMPforcing axiomsNamba forcing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1539 - 1565
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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