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Dependences between definitions of finiteness. II. (English) Zbl 0804.03044

The paper under review is a continuation of Part I [the author and the reviewer, ibid. 38(113), No. 3, 389-397 (1988; Zbl 0667.03040)]. In set theory without the axiom of choice various definitions of finiteness are known to be independent but there are at most 9 types of simultaneous occurrences of different types of finite sets. The result is improved by giving explicit constructions of various types of finite sets and by constructing models of ZF and/or ZFU where certain occurrences are realized.

MSC:

03E99 Set theory
03E25 Axiom of choice and related propositions

Citations:

Zbl 0667.03040
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References:

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