Some structural similarities between uncountable sets, powersets and the universe

Mathematical Logic Quarterly 68 (2):136-148 (2022)
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Abstract

We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras, for a regular cardinal κ, and (the class of subclasses of the universe V), endowed with some ideals, especially the ideal for, and the ideal of sets V for.

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10.1002/malq.202100010

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Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Model Theory: An Introduction.David Marker - 2003 - Bulletin of Symbolic Logic 9 (3):408-409.
Localizing the axioms.Athanassios Tzouvaras - 2010 - Archive for Mathematical Logic 49 (5):571-601.
Positive set-operators of low complexity.Athanossios Tzouvaras - 2003 - Mathematical Logic Quarterly 49 (3):284.
What is so special with the powerset operation?Athanassios Tzouvaras - 2004 - Archive for Mathematical Logic 43 (6):723-737.

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