Search results for "minimalist foundation"

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Finiteness in a Minimalist Foundation

2008

We analyze the concepts of finite set and finite subset from the perspective of a minimalist foundational theory which has recently been introduced by Maria Emilia Maietti and the second author. The main feature of that theory and, as a consequence, of our approach is compatibility with other foundational theories such as Zermelo-Fraenkel set theory, Martin-Lof's intuitionistic Type Theory, topos theory, Aczel's CZF, Coquand's Calculus of Constructions. This compatibility forces our arguments to be constructive in a strong sense: no use is made of powerful principles such as the axiom of choice, the power-set axiom, the law of the excluded middle.

General set theoryMorse–Kelley set theoryNon-well-founded set theoryZermelo–Fraenkel set theoryConstructive set theoryminimalist foundation; finite sets; finite subsets; type theory; constructive mathematicsconstructive mathematicsfinite subsetsUrelementMathematics::LogicType theorytype theoryComputer Science::Logic in Computer ScienceAxiom of choicefinite setsminimalist foundationMathematical economicsMathematics
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