Publications de l'Institut Mathématique, Nouvelle Série Vol. 82(96), pp. 155–163 (2007) 

FINSET: A SYNTACTICAL DEFINITION OF FINITE SETSSlavisa B. PresicMatematicki fakultet, Beograd, SerbiaAbstract: We state Finset, by which one founds the notion of finite sets in a syntactical way. Any finite set $\{a_1,a_2,\dots,a_n\}$ is defined as a well formed term of the form $S(a_1+(a_2+(\cdots+(a_{n1}+a_n)\cdots)))$, where $+$ is a binary and $S$ a unary operational symbol. Related to the operational symbol $+$ the termsubstitutions (1) are supposed. Definition of finite sets is called syntactical because by two algorithms Setalg and Calc (below) one can effectively establish whether any given setterms are equal or not equal.
All other notions of finite sets, like $\in$, ordered pair, Cartesian product, relation, function, cardinal number are defined as a corresponding term. Each of these definitions is recursive. For instance, $\in$ is defined by \begin{align*} &x\in S(a_1)\quad\text{iff}\quad x=a_1
Keywords: finite set, algorithm, syntactical definition Classification (MSC2000): 03E30 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Feb 2008. This page was last modified: 26 Feb 2008.
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