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Mechanizing set theory: Cardinal arithmetic and the axiom of choice
 Journal of Automated Reasoning
, 1996
"... Abstract. Fairly deep results of ZermeloFrænkel (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 resu ..."
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Cited by 16 (9 self)
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Abstract. Fairly deep results of ZermeloFrænkel (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, orderisomorphisms, 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 Wellordering 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
Tool Support for Logics of Programs
 Mathematical Methods in Program Development: Summer School Marktoberdorf 1996, NATO ASI Series F
, 1996
"... Proof tools must be well designed if they... ..."
LetPolymorphism and Eager Type Schemes
 In TAPSOFT '97: Theory and Practice of Software Development
, 1997
"... . This paper presents an algorithm for polymorphic type inference involving the let construct of ML in the context of higher order abstract syntax. It avoids the polymorphic closure operation of the algorithm W of Damas and Milner by using a uniform treatment of type variables at the metalevel ..."
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. This paper presents an algorithm for polymorphic type inference involving the let construct of ML in the context of higher order abstract syntax. It avoids the polymorphic closure operation of the algorithm W of Damas and Milner by using a uniform treatment of type variables at the metalevel. The basic technique of the algorithm facilitates the declarative formulation of type inference as goaldirected proofsearch in a logical frameworks setting. 1 Introduction Formulations and algorithms for the assignment of principal types to untyped  terms have long existed before Damas and Milner [2] extended it to involve the polymorphic let construct of functional programming languages (ML). They formulated a declarative, prooftheoretic calculus for the ML type system, given here in Figure 1. Unfortunately, this calculus does not by itself lead directly to an inference algorithm that yields principal type schemes. For this purpose the algorithm "W " was given. Algorithm W requires...
Mechanising Set Theory: Cardinal Arithmetic and the Axiom of Choice
, 1995
"... A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the ..."
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A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the Mizar journal [6]. However,