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## Fundamenta Mathematicae

2013 | 220 | 3 | 207-216
Tytuł artykułu

### Partial choice functions for families of finite sets

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Let m ≥ 2 be an integer. We show that ZF + "Every countable set of m-element sets has an infinite partial choice function" is not strong enough to prove that every countable set of m-element sets has a choice function, answering an open question from . (Actually a slightly stronger result is obtained.) The independence result in the case where m = p is prime is obtained by way of a permutation (Fraenkel-Mostowski) model of ZFA, in which the set of atoms (urelements) has the structure of a vector space over the finite field $𝔽_{p}$. The use of atoms is then eliminated by citing an embedding theorem of Pincus. In the case where m is not prime, suitable permutation models are built from the models used in the prime cases.
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207-216
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wydano
2013
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autor
• Department of Mathematics & Statistics, University of Missouri-Kansas City, Kansas City, MO 64110, U.S.A.
autor
• Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
• Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, U.S.A.
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