Amorphous set
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Amorphous set
In set theory, an amorphous set is an infinite set which is not the disjoint union of two infinite subsets. Amorphous sets are Dedekind-finite. There are no such sets, if the axiom of choice is assumed. A model of ZF in which an amorphous set exists was given by Azriel Levy, using an earlier model of Mostowski.
References
- A. Levy: The independence of various definition of finiteness, Fund. Math., 46(1958), 1–13.
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