Odd-sized partitions of Russell-sets

Mathematical Logic Quarterly 56 (2):185-190 (2010)
  Copy   BIBTEX

Abstract

In the setting of ZF, i.e., Zermelo–Fraenkel set theory without the Axiom of Choice , we study partitions of Russell-sets into sets each with exactly n elements , for some integer n. We show that if n is odd, then a Russell-set X has an n -ary partition if and only if |X | is divisible by n. Furthermore, we establish that it is relative consistent with ZF that there exists a Russell-set X such that |X | is not divisible by any finite cardinal n > 1

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,726

External links

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

Through your library

Similar books and articles

Cantor’s Theorem May Fail for Finitary Partitions.Guozhen Shen - forthcoming - Journal of Symbolic Logic:1-18.
The independence of Ramsey's theorem.E. M. Kleinberg - 1969 - Journal of Symbolic Logic 34 (2):205-206.
Parameterized partition relations on the real numbers.Joan Bagaria & Carlos A. Di Prisco - 2009 - Archive for Mathematical Logic 48 (2):201-226.
Compact Metric Spaces and Weak Forms of the Axiom of Choice.E. Tachtsis & K. Keremedis - 2001 - Mathematical Logic Quarterly 47 (1):117-128.
Finiteness Classes and Small Violations of Choice.Horst Herrlich, Paul Howard & Eleftherios Tachtsis - 2016 - Notre Dame Journal of Formal Logic 57 (3):375-388.
Divisibility of dedekind finite sets.David Blair, Andreas Blass & Paul Howard - 2005 - Journal of Mathematical Logic 5 (1):49-85.
On hereditarily small sets in ZF.M. Randall Holmes - 2014 - Mathematical Logic Quarterly 60 (3):228-229.
Flat sets.Arthur D. Grainger - 1994 - Journal of Symbolic Logic 59 (3):1012-1021.

Analytics

Added to PP
2013-12-01

Downloads
12 (#1,121,595)

6 months
3 (#1,254,220)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references