Abstract
Some new double analogues of induction and transfinite recursion are given which yields a relatively simple proof of a result of Robert Cowen, [2] which in turn is a strengthening of an earlier result of Smullyan [1], which in turn gives a unified approach to Zorn's Lemma, the transfinite recursion theorem and certain results about ordinal numbers.
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References
R. Smullyan, On transfinite recursion, Transactions of the New York Academy of Sciences (1966), pp. 175–185.
R. Cowen, Superinductive classes in class-set theory, Notre Dame Journal of Formal Logic, Volume XII, Number 1, January 1971, pp. 62–68.
P. R. Halmos, Naive Set Theory, D. Van Nostraud Company, Inc., Princeton, 1968, p. 51.
K. Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory, Annals of Mathematics Studies, Volume 3, Princeton University Press, Princeton (1961).
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Smullyan, R.M. Some new double induction and superinduction principles. Stud Logica 49, 23–30 (1990). https://doi.org/10.1007/BF00401551
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DOI: https://doi.org/10.1007/BF00401551