The First-Order Structure of Weakly Dedekind-Finite Sets

Journal of Symbolic Logic 70 (4):1161 - 1170 (2005)
  Copy   BIBTEX

Abstract

We show that infinite sets whose power-sets are Dedekind-finite can only carry N₀-categorical first order structures. We identify other subclasses of this class of Dedekind-finite sets, and discuss their possible first order structures

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1129642121

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,423

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

The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck - 1998 - In Matthias Schirn (ed.), Philosophy of Mathematics Today. Oxford University Press.
Expansion of a model of a weakly o-minimal theory by a family of unary predicates.Bektur Sembiuly Baizhanov - 2001 - Journal of Symbolic Logic 66 (3):1382-1414.
The ordertype of β-r.E. Sets.Klaus Sutner - 1990 - Journal of Symbolic Logic 55 (2):573-576.
First-order Gödel logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
A General Setting for Dedekind's Axiomatization of the Positive Integers.George Weaver - 2011 - History and Philosophy of Logic 32 (4):375-398.
Weakly semirecursive sets.Carl G. Jockusch & James C. Owings - 1990 - Journal of Symbolic Logic 55 (2):637-644.
Indifferent sets for genericity.Adam R. Day - 2013 - Journal of Symbolic Logic 78 (1):113-138.
Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry.John P. Burgess - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
Finitely constrained classes of homogeneous directed graphs.Brenda J. Latka - 1994 - Journal of Symbolic Logic 59 (1):124-139.
Axiom systems for first order logic with finitely many variables.James S. Johnson - 1973 - Journal of Symbolic Logic 38 (4):576-578.
P versus np and computability theoretic constructions in complexity theory over algebraic structures.Gunther Mainhardt - 2004 - Journal of Symbolic Logic 69 (1):39-64.
Hereditary undecidability of some theories of finite structures.Ross Willard - 1994 - Journal of Symbolic Logic 59 (4):1254-1262.

Analytics

Added to PP
2010-08-24

Downloads
25 (#618,847)

6 months
4 (#800,606)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A dedekind finite borel set.Arnold W. Miller - 2011 - Archive for Mathematical Logic 50 (1-2):1-17.

Add more citations

References found in this work

ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
The structure of amorphous sets.J. K. Truss - 1995 - Annals of Pure and Applied Logic 73 (2):191-233.
Some Aspects and Examples of Infinity Notions.J. W. Degen - 1994 - Mathematical Logic Quarterly 40 (1):111-124.
On o-amorphous sets.P. Creed & J. K. Truss - 2000 - Annals of Pure and Applied Logic 101 (2-3):185-226.

View all 6 references / Add more references