Research and Innovation Articles
Published 2011-11-23
Keywords
- recursion,
- induction,
- well-founded order
How to Cite
Parra-Londoño, C., & Mejía-Guzmán, D. (2011). Recursion, induction and well-founded orders. Revista Integración, Temas De matemáticas, 29(2), 143–150. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2555
Abstract
Based on the characterization of the set of natural numbers by the recursion property, developed in [2], we prove in a general setting that the properties of recursion, induction and well-foundedness are equivalent for a given set. This result is extended to classes and is used to give another proof of the characterization of the set of natural numbers by recursion.
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References
[1] Kunen K., Set Theory. An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980.
[2] Lawvere F.W., “An elementary theory of the category of sets (long version) with commentary”, Repr. Theory Appl. Categ. 11 (2005), 1-35.
[3] Levy A., Basic Set Theory, Dover, New York, 2002.
[2] Lawvere F.W., “An elementary theory of the category of sets (long version) with commentary”, Repr. Theory Appl. Categ. 11 (2005), 1-35.
[3] Levy A., Basic Set Theory, Dover, New York, 2002.