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CANONICAL MODELS FOR FRAGMENTS OF THE AXIOM OF CHOICE

Published online by Cambridge University Press:  19 June 2017

PAUL LARSON  and
JINDŘICH ZAPLETAL
PAUL LARSON
Affiliation:
DEPARTMENT OF MATHEMATICS MIAMI UNIVERSITY OXFORD, OH45056, USAE-mail: larsonpb@miamioh.edu
JINDŘICH ZAPLETAL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF FLORIDA PO BOX 118105 GAINESVILLE, FL32611, USAE-mail: zapletal@math.ufl.edu
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Abstract

We develop technology for investigation of natural forcing extensions of the model $L\left( \mathbb{R} \right)$ which satisfy such statements as “there is an ultrafilter” or “there is a total selector for the Vitali equivalence relation”. The technology reduces many questions about ZF implications between consequences of the Axiom of Choice to natural ZFC forcing problems.

Keywords

03E1703E40Axioms of Choiceultrafilters equivalence relations
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 2 , June 2017 , pp. 489 - 509
Copyright
Copyright © The Association for Symbolic Logic 2017 

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