Premium
A theory of sets with the negation of the axiom of infinity
Author(s) -
Baratella Stefano,
Ferro Ruggero
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390138
Subject(s) - negation , mathematics , bijection , axiom , infinity , zermelo–fraenkel set theory , axiom of choice , power set , set (abstract data type) , urelement , fragment (logic) , set theory , discrete mathematics , algorithm , computer science , mathematical analysis , geometry , programming language
In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a non‐standard development. MSC: 03E30, 03E35.