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THE LOGIC OF COMPARATIVE CARDINALITY

Part of: Set theory General logic Algebraic logic

Published online by Cambridge University Press:  22 June 2020

YIFENG DING ,
MATTHEW HARRISON-TRAINOR  and
WESLEY H. HOLLIDAY
YIFENG DING
Affiliation:
GROUP IN LOGIC AND THE METHODOLOGY OF SCIENCE UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA94720, USAE-mail: yf.ding@berkeley.edu
MATTHEW HARRISON-TRAINOR
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS, VICTORIA UNIVERSITY OF WELLINGTON, 6140NEW ZEALANDE-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, CA94720, USAE-mail: wesholliday@berkeley.edu
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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.

Keywords

cardinality comparisonsqualitative probabilityBoolean algebrafields of sets

MSC classification

Primary: 03B60: Other nonclassical logic
Secondary: 03E10: Ordinal and cardinal numbers 03G05: Boolean algebras
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 972 - 1005
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Copyright
© The Association for Symbolic Logic 2020

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