Notre Dame Journal of Formal Logic

The Consistency Strength of M P C C C ( R )

George Leibman


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 .

Article information

Notre Dame J. Formal Logic, Volume 51, Number 2 (2010), 181-193.

First available in Project Euclid: 11 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results 03E40: Other aspects of forcing and Boolean-valued models

forcing forcing axioms modal logic


Leibman, George. The Consistency Strength of $\mathrm{MP_{CCC}}(\mathbb{R})$. Notre Dame J. Formal Logic 51 (2010), no. 2, 181--193. doi:10.1215/00294527-2010-011.

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