On the Well-ordering Principle and the Principle of Finite Induction
DOI:
https://doi.org/10.31686/ijier.vol11.iss5.3922Keywords:
set of natural numbers, set of integers, Well-ordering Principle, Principle of Finite InductionAbstract
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.
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References
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),
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S. Mac Lane and Birkhoff, Algebra, Sixth Printing, Macmillan, New York, 1971.
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Accepted 2023-05-05
Published 2023-05-09
