When does every definable nonempty set have a definable element?

&
Mathematical Logic Quarterly 65 (4):407-411 (2019)
  Copy   BIBTEX

Abstract

The assertion that every definable set has a definable element is equivalent over to the principle, and indeed, we prove, so is the assertion merely that every Π2‐definable set has an ordinal‐definable element. Meanwhile, every model of has a forcing extension satisfying in which every Σ2‐definable set has an ordinal‐definable element. Similar results hold for and and other natural instances of.

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.201700035

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,497

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

Definable homomorphisms of abelian groups in o-minimal structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.
Pointwise definable models of set theory.Joel David Hamkins, David Linetsky & Jonas Reitz - 2013 - Journal of Symbolic Logic 78 (1):139-156.
A remark on divisibility of definable groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.
A weakly definable type which is not definable.James H. Schmerl - 1993 - Archive for Mathematical Logic 32 (6):463-468.
On compactifications and the topological dynamics of definable groups.Jakub Gismatullin, Davide Penazzi & Anand Pillay - 2014 - Annals of Pure and Applied Logic 165 (2):552-562.
Definability of groups in ℵ₀-stable metric structures.Itaï Ben Yaacov - 2010 - Journal of Symbolic Logic 75 (3):817-840.
Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function.Ricardo Bianconi - 1997 - Journal of Symbolic Logic 62 (4):1173-1178.
Presburger arithmetic and recognizability of sets of natural numbers by automata: New proofs of Cobham's and Semenov's theorems.Christian Michaux & Roger Villemaire - 1996 - Annals of Pure and Applied Logic 77 (3):251-277.
Groups, group actions and fields definable in first‐order topological structures.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (6):449-467.
Tame Topology over dp-Minimal Structures.Pierre Simon & Erik Walsberg - 2019 - Notre Dame Journal of Formal Logic 60 (1):61-76.
Definable subgroups of measure algebras.Alexander Berenstein - 2006 - Mathematical Logic Quarterly 52 (4):367-374.
Finitely axiomatizable ω-categorical theories and the Mazoyer hypothesis.David Lippel - 2005 - Journal of Symbolic Logic 70 (2):460-472.
Definability of groups in ℵ₀-stable metric structures.Itaï Yaacov - 2010 - Journal of Symbolic Logic 75 (3):817-840.
On the Type-Definability of the Binding Group in Simple Theories.Bradd Hart & Ziv Shami - 2005 - Journal of Symbolic Logic 70 (2):379 - 388.
λ-Definability on free algebras.Marek Zaionc - 1991 - Annals of Pure and Applied Logic 51 (3):279-300.

Analytics

Added to PP
2019-12-13

Downloads
15 (#953,911)

6 months
8 (#373,162)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joel David Hamkins
Oxford University

Citations of this work

Add more citations

References found in this work

A simple maximality principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Pointwise definable models of set theory.Joel David Hamkins, David Linetsky & Jonas Reitz - 2013 - Journal of Symbolic Logic 78 (1):139-156.

Add more references