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ON RESURRECTION AXIOMS

Published online by Cambridge University Press:  22 April 2015

KONSTANTINOS TSAPROUNIS
KONSTANTINOS TSAPROUNIS*
Affiliation:
DEPARTMENT OF LOGIC, HISTORY & PHILOSOPHY OF SCIENCE UNIVERSITY OF BARCELONA 08001 BARCELONA, SPAINE-mail: kostas.tsap@gmail.com
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Abstract

The resurrection axioms are forms of forcing axioms that were introduced recently by Hamkins and Johnstone, who developed on earlier ideas of Chalons and Veličković. In this note, we introduce a stronger form of resurrection (which we call unbounded resurrection) and show that it gives rise to families of axioms which are consistent relative to extendible cardinals, and which imply the strongest known instances of forcing axioms, such as Martin’s Maximum++. In addition, we study the unbounded resurrection postulates in terms of consistency lower bounds, obtaining, for example, failures of the weak square principle.

Keywords

03E3503E5503E57Forcing axiomsResurrection axiomsExtendible cardinals

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015 , pp. 587 - 608
Copyright
Copyright © The Association for Symbolic Logic 2015 

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