Mechanizing set theory: Cardinal arithmetic and the axiom of choice (1996)
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| Venue: | Journal of Automated Reasoning |
| Citations: | 15 - 9 self |
BibTeX
@ARTICLE{Paulson96mechanizingset,
author = {Lawrence C. Paulson and Krzysztof Grabczewski},
title = {Mechanizing set theory: Cardinal arithmetic and the axiom of choice},
journal = {Journal of Automated Reasoning},
year = {1996},
pages = {291--323}
}
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Abstract
Abstract. Fairly deep results of Zermelo-Frænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this result required developing theories of orders, order-isomorphisms, order types, ordinal arithmetic, cardinals, etc.; this covers most of Kunen, Set Theory, Chapter I. Furthermore, we have proved the equivalence of 7 formulations of the Well-ordering Theorem and 20 formulations of AC; this covers the first two chapters of Rubin and Rubin, Equivalents of the Axiom of Choice, and involves highly technical material. The definitions used in the proofs are
