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THE LOGIC OF COMPARATIVE CARDINALITY

Published online by Cambridge University Press:  22 June 2020

YIFENG DING
Affiliation:
GROUP IN LOGIC AND THE METHODOLOGY OF SCIENCE UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA 94720, USA E-mail: yf.ding@berkeley.edu
MATTHEW HARRISON-TRAINOR
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS, VICTORIA UNIVERSITY OF WELLINGTON, 6140 NEW ZEALAND E-mail: matthew.harrisontrainor@vuw.ac.nz
WESLEY H. HOLLIDAY
Affiliation:
DEPARTMENT OF PHILOSOPHY AND GROUP IN LOGIC AND THE METHODOLOGY OF SCIENCE, UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA 94720, USA E-mail: wesholliday@berkeley.edu

Abstract

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.

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Articles
Copyright
© The Association for Symbolic Logic 2020

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