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Finite-to-one maps

Journal of Symbolic Logic 68 (4):1251-1253 (2003)

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  1. Generalizations of Cantor's Theorem in ZF.Guozhen Shen - 2017 - Mathematical Logic Quarterly 63 (5):428-436.
    A set x is Dedekind infinite if there is an injection from ω into x; otherwise x is Dedekind finite. A set x is power Dedekind infinite if math formula, the power set of x, is Dedekind infinite; otherwise x is power Dedekind finite. For a set x, let pdfin be the set of all power Dedekind finite subsets of x. In this paper, we prove in math formula two generalizations of Cantor's theorem : The first one is that for (...)
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