One of the most important results in basic set theory is without doubt Cantor’s Theorem which states that the power set of anyset X is strictly bigger than X itself. Specker once stated, without providing a proof, that a generalization is possible: for any natural exponentm, there is a natural number N for which if X has at least N distinct elements, then the power set of X is strictly bigger than X^m. The aim of this paper is to formalize and prove Specker’s claim and to provide a way to compute the values of N for which the theorem holds.
A Generalization of Cantor’s Theorem
Giulio Fellin
2018-01-01
Abstract
One of the most important results in basic set theory is without doubt Cantor’s Theorem which states that the power set of anyset X is strictly bigger than X itself. Specker once stated, without providing a proof, that a generalization is possible: for any natural exponentm, there is a natural number N for which if X has at least N distinct elements, then the power set of X is strictly bigger than X^m. The aim of this paper is to formalize and prove Specker’s claim and to provide a way to compute the values of N for which the theorem holds.
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