Martin’s Maximum and definability in H

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

In [P. Larson, Martin’s Maximum and the axiom , Ann. Pure App. Logic 106 135–149], we modified a coding device from [W.H. Woodin, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, Walter de Gruyter & Co, Berlin, 1999] and the consistency proof of Martin’s Maximum from [M. Foreman, M. Magidor, S. Shelah, Martin’s Maximum. saturated ideals, and non-regular ultrafilters. Part I, Annal. Math. 127 1–47] to show that from a supercompact limit of supercompact cardinals one could force Martin’s Maximum to hold while the axiom fails. Here we modify that argument to prove a stronger fact, that Martin’s Maximum is consistent with the existence of a wellordering of the reals definable in H without parameters, from the same large cardinal hypothesis. In doing so we give a much simpler proof of the original result

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Citations of this work

Characterizing All Models in Infinite Cardinalities.Lauri Keskinen - 2013 - Annals of Pure and Applied Logic 164 (3):230-250.
On a Class of Maximality Principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.
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References found in this work

Set Mapping Reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
The Size of $\tilde{T}$.Paul Larson - 2000 - Archive for Mathematical Logic 39 (7):541-568.
Guessing and Non-Guessing of Canonical Functions.David Asperó - 2007 - Annals of Pure and Applied Logic 146 (2):150-179.
The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.
Martin's Maximum and The.Paul Larson - 2000 - Annals of Pure and Applied Logic 106 (1-3):135-149.

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