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2010 The Consistency Strength of M P C C C ( R )
George Leibman
Notre Dame J. Formal Logic 51(2): 181-193 (2010). DOI: 10.1215/00294527-2010-011

Abstract

The Maximality Principle M P C C C is a scheme which states that if a sentence of the language of ZFC is true in some CCC forcing extension V P , and remains true in any further CCC-forcing extension of V P , then it is true in all CCC-forcing extensions of V, including V itself. A parameterized form of this principle, M P C C C ( R ) , makes this assertion for formulas taking real parameters. In this paper, we show that M P C C C ( R ) has the same consistency strength as ZFC, solving an open problem of Hamkins. We extend this result further to parameter sets larger than R .

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George Leibman. "The Consistency Strength of M P C C C ( R ) ." Notre Dame J. Formal Logic 51 (2) 181 - 193, 2010. https://doi.org/10.1215/00294527-2010-011

Information

Published: 2010
First available in Project Euclid: 11 June 2010

zbMATH: 1205.03059
MathSciNet: MR2667905
Digital Object Identifier: 10.1215/00294527-2010-011

Subjects:
Primary: 03E35, 03E40

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 2 • 2010
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