科研之友
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摘要
A set A is Dedekind infinite if there is a one-to-one function from omega into A. A set A is weakly Dedekind infinite if there is a function from A onto omega; otherwise A is weakly Dedekind finite. For a set M, let dfin*(M) denote the set of all weakly Dedekind finite subsets of M. In this paper, we prove, in Zermelo-Fraenkel (ZF) set theory, that vertical bar dfin*(M)vertical bar < vertical bar P(M)vertical bar if dfin*(M) is Dedekind infinite, whereas vertical bar dfin*(M)vertical bar < vertical bar P(M)vertical bar cannot be proved from ZF for an arbitrary M.
- 出版日期2014
