Arithmetic definability by formulas with two quantifiers

Journal of Symbolic Logic 57 (1):1-11 (1992)
  Copy   BIBTEX

Abstract

We give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson

Categories

Keywords

Reprint years

DOI

10.2307/2275172

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

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 Hierarchy Theorem for Second Order Generalized Quantifiers.Juha Kontinen - 2006 - Journal of Symbolic Logic 71 (1):188 - 202.
Characterizing Definability of Second-Order Generalized Quantifiers.Juha Kontinen & Jakub Szymanik - 2011 - In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Definability in number fields.S. P. Tung - 1987 - Journal of Symbolic Logic 52 (1):152-155.
One Connection between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers.Dorit Ben Shalom - 2003 - Journal of Logic, Language and Information 12 (1):47-52.
On the expressive power of monotone natural language quantifiers over finite models.Jouko Väänänen & Dag Westerståhl - 2002 - Journal of Philosophical Logic 31 (4):327-358.
Descriptive complexity of finite structures: Saving the quantifier rank.Oleg Pikhurko & Oleg Verbitsky - 2005 - Journal of Symbolic Logic 70 (2):419-450.

Analytics

Added to PP
2009-01-28

Downloads
43 (#361,277)

6 months
7 (#411,886)

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

Definability on Formulas With Single Quantifier.Shih-Ping Tung - 1988 - Mathematical Logic Quarterly 34 (2):105-108.
Definability on Formulas With Single Quantifier.Shih-Ping Tung - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (2):105-108.

Add more references