Journal of Symbolic Logic 85 (3):972-1005 (2020)

Yifeng Ding
University of California, Berkeley
Wesley H. Holliday
University of California, Berkeley
This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and complementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under the Cantorian definition of relative size in terms of injections.
Keywords cardinality comparisons  Boolean algebra  set theory  Cantor
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DOI 10.1017/jsl.2019.67
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Qualitative Probability as an Intensional Logic.Peter Gärdenfors - 1975 - Journal of Philosophical Logic 4 (2):171 - 185.
Axiomatizing the Logic of Comparative Probability.John P. Burgess - 2010 - Notre Dame Journal of Formal Logic 51 (1):119-126.

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