Weak choice principles
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- by Omar De la Cruz and Carlos Augusto Di Prisco PDF
- Proc. Amer. Math. Soc. 126 (1998), 867-876 Request permission
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.References
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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
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 867-876
- MSC (1991): Primary 03E25, 04A25
- DOI: https://doi.org/10.1090/S0002-9939-98-04103-3
- MathSciNet review: 1422860