6533b860fe1ef96bd12c3bc9

RESEARCH PRODUCT

Finiteness in a Minimalist Foundation

Giovanni SambinFrancesco Ciraulo

subject

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

description

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.

yearjournalcountryeditionlanguage
2008-05-06
https://doi.org/10.1007/978-3-540-68103-8_4