Reconsidering Pairs and Functions as Sets

We give representations for ordered pairs and functions in set theory with the property that ordered pairs are functions from the finite ordinal 2. We conjecture that these representations are useful for formalized mathematics since certain isomorphic sets are identified. The definitions, theorems a...

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Bibliographic Details
Published inJournal of automated reasoning Vol. 55; no. 3; pp. 199 - 210
Main Author Brown, Chad E.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2015
Subjects
Artificial Intelligence
Computer Science
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Symbolic and Algebraic Manipulation
Set theory
Ordered pairs
Functions
Higher-order theorem proving
Simple type theory
Higher-order logic
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Summary:We give representations for ordered pairs and functions in set theory with the property that ordered pairs are functions from the finite ordinal 2. We conjecture that these representations are useful for formalized mathematics since certain isomorphic sets are identified. The definitions, theorems and proofs have been formalized in the proof assistant Coq using only the simply typed features of Coq. We describe the development within the context of an intuitionistic simply typed (higher-order) version of (well-founded) Zermelo-Fraenkel set theory without the axiom of infinity.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-015-9340-6