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Martin’s Maximum and definability in H

Paul B. Larson

Annals of Pure and Applied Logic 156 (1):110-122 (2008)

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On a class of maximality principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.details We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the principle MP\\) (...) Download Export citation Bookmark 1 citation
Bounded Martin’s Maximum with an Asterisk.David Asperó & Ralf Schindler - 2014 - Notre Dame Journal of Formal Logic 55 (3):333-348.details We isolate natural strengthenings of Bounded Martin’s Maximum which we call ${\mathsf{BMM}}^{}$ and $A-{\mathsf{BMM}}^{,++}$, and we investigate their consequences. We also show that if $A-{\mathsf{BMM}}^{,++}$ holds true for every set of reals $A$ in $L$, then Woodin’s axiom $$ holds true. We conjecture that ${\mathsf{MM}}^{++}$ implies $A-{\mathsf{BMM}}^{,++}$ for every $A$ which is universally Baire. Download Export citation Bookmark
Characterizing all models in infinite cardinalities.Lauri Keskinen - 2013 - Annals of Pure and Applied Logic 164 (3):230-250.details Fix a cardinal κ. We can ask the question: what kind of a logic L is needed to characterize all models of cardinality κ up to isomorphism by their L-theories? In other words: for which logics L it is true that if any models A and B of cardinality κ satisfy the same L-theory then they are isomorphic?It is always possible to characterize models of cardinality κ by their Lκ+,κ+-theories, but we are interested in finding a “small” logic L, i.e., (...) Download Export citation Bookmark 2 citations

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