Compact and Loeb Hausdorff spaces in equation image and the axiom of choice for families of finite sets

Mathematical Logic Quarterly 58 (3):130-138 (2012)
  Copy   BIBTEX

Abstract

Given a set X, equation image denotes the statement: “equation image has a choice set” and equation image denotes the family of all closed subsets of the topological space equation image whose definition depends on a finite subset of X. We study the interrelations between the statements equation image equation image equation image equation image and “equation imagehas a choice set”. We show: equation image iff equation image iff equation image has a choice set iff equation image. equation image iff for every set X, equation image has a choice set. equation image does not imply “equation image has a choice set equation image implies equation image but equation image does not imply equation image.We also show that “For every setX, “equation imagehas a choice set” iff “for every setX, equation imagehas a choice set” iff “for every productequation imageof finite discrete spaces,equation image has a choice set”.

Categories

Keywords

Reprint years

DOI

10.1002/malq.201020039

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,611

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Strengths and Weaknesses of LH Arithmetic.Chris Pollett & Randall Pruim - 2002 - Mathematical Logic Quarterly 48 (2):221-243.
Infinite games in the Cantor space and subsystems of second order arithmetic.Takako Nemoto, MedYahya Ould MedSalem & Kazuyuki Tanaka - 2007 - Mathematical Logic Quarterly 53 (3):226-236.
Remarks on gaps in Dense (Q) / nwd.Teppo Kankaanpää - 2013 - Mathematical Logic Quarterly 59 (1-2):51-61.
Models of expansions of equation image with no end extensions.Saharon Shelah - 2011 - Mathematical Logic Quarterly 57 (4):341-365.
A p-adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4):263-280.
On the Additive Group Structure of the Nonstandard Models of the Theory of Integers.Hasan Dalgin, Labib Haddad & Mehmet Terziler - 2002 - Mathematical Logic Quarterly 48 (3):403-412.
Thin equivalence relations in scaled pointclasses.Ralf Schindler & Philipp Schlicht - 2011 - Mathematical Logic Quarterly 57 (6):615-620.
A p‐adic probability logic.Angelina Ilić-Stepić, Zoran Ognjanović, Nebojša Ikodinović & Aleksandar Perović - 2012 - Mathematical Logic Quarterly 58 (4-5):263-280.
Remarks on gaps in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathrm{Dense}(\mathbb {Q})/\mathbf {nwd}}$\end{document}.Teppo Kankaanpää - 2013 - Mathematical Logic Quarterly 59 (1-2):51-61.
Weak forms of the Regularity Principle in the presence of equation image.Charalampos Cornaros - 2013 - Mathematical Logic Quarterly 59 (1-2):84-100.
There is No Low Maximal D.C.E. Degree.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2000 - Mathematical Logic Quarterly 46 (3):409-416.
Superatomic Boolean algebras constructed from strongly unbounded functions.Juan Carlos Martínez & Lajos Soukup - 2011 - Mathematical Logic Quarterly 57 (5):456-469.
Computably Enumerable Reals and Uniformly Presentable Ideals.S. A. Terwijn & R. Downey - 2002 - Mathematical Logic Quarterly 48 (S1):29-40.
The Bergman‐Shelah preorder on transformation semigroups.Zak Mesyan, James D. Mitchell, Michał Morayne & Yann H. Péresse - 2012 - Mathematical Logic Quarterly 58 (6):424-433.
De Morgan Heyting algebras satisfying the identity xn ≈ x.Valeria Castaño & Marcela Muñoz Santis - 2011 - Mathematical Logic Quarterly 57 (3):236-245.

Analytics

Added to PP
2013-10-31

Downloads
54 (#298,271)

6 months
8 (#373,162)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

The structure of amorphous sets.J. K. Truss - 1995 - Annals of Pure and Applied Logic 73 (2):191-233.
Products of compact spaces in the least permutation model.Norbert Brunner - 1985 - Mathematical Logic Quarterly 31 (25‐28):441-448.
Products of Compact Spaces in the Least Permutation Model.Norbert Brunner - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):441-448.

Add more references