Weak choice principles-Reference-Cited by-同舟云学术

Weak choice principles

Published:1998 Issue:3 Volume:126 Page:867-876
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

De la Cruz Omar,Di Prisco Carlos

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1998-126-03/S0002-9939-98-04103-3/S0002-9939-98-04103-3.pdf

Reference13 articles.

1. Ramsey’s theorem in the hierarchy of choice principles;Blass, Andreas;J. Symbolic Logic,1977

2. Sequential compactness and the axiom of choice;Brunner, Norbert;Notre Dame J. Formal Logic,1983

3. [G] Gonzalez, C., Partitioning an Infinite Set, Preprint (1994).

4. Studies in Logic and the Foundations of Mathematics, Vol. 75;Jech, Thomas J.,1973

5. A class of orthogonal functions on plane curves;Jackson, Dunham;Ann. of Math. (2),1939

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Some implications of Ramsey Choice for families of $$\varvec{n}$$-element sets;Archive for Mathematical Logic;2022-12-16

2. Denumerable cellular families in $\mathbf{ZF}$;Portugaliae Mathematica;2022-01-17

3. THE RELATION BETWEEN TWO DIMINISHED CHOICE PRINCIPLES;The Journal of Symbolic Logic;2021-02-15

4. On variants of the principle of consistent choices, the minimal cover property and the 2-compactness of generalized Cantor cubes;Topology and its Applications;2017-03