On the Well-ordering Principle and the Principle of Finite Induction
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Author
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- Keywords:
- Array, Array, Array, Array
- Abstract
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In this note the equivalence among the Well-ordering Principle, the Principle of Finite Induction and certain natural conditions concerning the set of integers is discussed, thereby clarifying facts encountered in the literature.
- References
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G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, Eighth Printing, Macmillan, New York, 1971.
F. Cajori, Origin of the Name ”Mathematical Induction”, Amer. Math. Monthly 25 (1918), 197-201. DOI: https://doi.org/10.1080/00029890.1918.11998417
F.W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 1964), 1506-1511. DOI: https://doi.org/10.1073/pnas.52.6.1506
F.W. Lawvere, An elementary theory of the category of sets (long version) with commentary, Reprints in Theory and Applications of Categories, No. 11 (2005),
-35.
S. Mac Lane and Birkhoff, Algebra, Sixth Printing, Macmillan, New York, 1971.
C.P. Milies e S.P. Coelho, Nu´meros: Uma Introdu¸ca˜o `a Matema´tica. Editora da Universidade de S˜ao Paulo, S˜ao Paulo, 1998.
G. Peano, Arithmeticas principia, novo methodo exposita, Turin, 1889.
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- 2023-05-09
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