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Weak choice principles

Author(s): Omar De la Cruz; Carlos Augusto Di Prisco
Journal: Proc. Amer. Math. Soc. 126 (1998), 867-876.
MSC (1991): Primary 03E25, 04A25
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Abstract: We consider several weak forms of the Axiom of Choice obtained debilitating some well known choice principles. Implication relations among them and independence results are established using, in some cases, permutation models or symmetric models. The relationship between Ramsey's Theorem and these choice principles is also explored, showing that, in this context, the known results are the best possible.

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Additional Information:

Omar De la Cruz
Affiliation: Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, Caracas 1020-A, Venezuela
Address at time of publication: Department of Mathematics, University of Florida, Gaines- ville, Florida 32611
Email: odlc@math.ufl.edu

Carlos Augusto Di Prisco
Affiliation: Department of Mathematics, Instituto Venezolano de Investigaciones Científicas, Apartado 21827, Caracas 1020-A, Venezuela
Email: cdiprisc@ivic.ivic.ve

DOI: 10.1090/S0002-9939-98-04103-3
PII: S 0002-9939(98)04103-3
Received by editor(s): February 28, 1996
Received by editor(s) in revised form: August 30, 1996
Additional Notes: The authors thank Carlos Gonzalez and David Pincus for conversations on the subject of this article
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1998, American Mathematical Society


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