Finitary Set Theory
Kirby, Laurence
Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, p. 227-244 / Harvested from Project Euclid
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I argue for the use of the adjunction operator (adding a single new element to an existing set) as a basis for building a finitary set theory. It allows a simplified axiomatization for the first-order theory of hereditarily finite sets based on an induction schema and a rigorous characterization of the primitive recursive set functions. The latter leads to a primitive recursive presentation of arithmetical operations on finite sets.
Publié le : 2009-07-15
Classification:  hereditarily finite sets,  primitive recursive set functions,  adjunction,  03C13,  03D20,  03E10,  03E30 
@article{1257862036,
     author = {Kirby, Laurence},
     title = {Finitary Set Theory},
     journal = {Notre Dame J. Formal Logic},
     volume = {50},
     number = {1},
     year = {2009},
     pages = { 227-244},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257862036}
}

Kirby, Laurence. Finitary Set Theory. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp.  227-244. http://gdmltest.u-ga.fr/item/1257862036/