The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal

Mathematical Logic Quarterly 51 (5):493-498 (2005)
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Abstract

The Necessary Maximality Principle for c. c. c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal.

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Joel David Hamkins
Oxford University

Citations of this work

Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
Tall cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
The modal logic of inner models.Tanmay Inamdar & Benedikt Löwe - 2016 - Journal of Symbolic Logic 81 (1):225-236.
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

Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
A simple maximality principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Generic absoluteness.Joan Bagaria & Sy Friedman - 2001 - Annals of Pure and Applied Logic 108 (1-3):3-13.

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