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EXISTENTIALLY CLOSED MODELS IN THE FRAMEWORK OF ARITHMETIC

Published online by Cambridge University Press:  10 May 2016

ZOFIA ADAMOWICZ ,
ANDRÉS CORDÓN-FRANCO  and
F. FÉLIX LARA-MARTÍN
ZOFIA ADAMOWICZ
Affiliation:
MATHEMATICAL INSTITUTE OF THE POLISH ACADEMY OF SCIENCES ŚNIADECKICH 8 00-956 WARSZAWA, POLANDE-mail:zosiaa@impan.pl
ANDRÉS CORDÓN-FRANCO
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE AND ARTIFICIAL INTELLIGENCE UNIVERSIDAD DE SEVILLA AVDA. REINA MERCEDES S/N 41012 SEVILLA, SPAINE-mail:acordon@us.es
F. FÉLIX LARA-MARTÍN
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE AND ARTIFICIAL INTELLIGENCE UNIVERSIDAD DE SEVILLA AVDA. REINA MERCEDES S/N 41012 SEVILLA, SPAINE-mail:fflara@us.es
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Abstract

We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.

Keywords

fragments of Peano arithmeticExistentially closed modelsTuring degrees of arithmetic theories
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 774 - 788
Copyright
Copyright © The Association for Symbolic Logic 2016 

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