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TWO-VARIABLE LOGIC HAS WEAK, BUT NOT STRONG, BETH DEFINABILITY

Part of: Model theory General logic

Published online by Cambridge University Press:  01 February 2021

HAJNAL ANDRÉKA  and
ISTVÁN NÉMETI
HAJNAL ANDRÉKA
Affiliation:
SET THEORY, LOGIC AND TOPOLOGY DEPARTMENT ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS BUDAPEST, REÁLTANODA ST. 13–15, H-1053, HUNGARYE-mail:andreka.hajnal@renyi.huE-mail:nemeti.istvan@renyi.hu
ISTVÁN NÉMETI
Affiliation:
SET THEORY, LOGIC AND TOPOLOGY DEPARTMENT ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS BUDAPEST, REÁLTANODA ST. 13–15, H-1053, HUNGARYE-mail:andreka.hajnal@renyi.huE-mail:nemeti.istvan@renyi.hu
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Abstract

We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong Beth definability property.

Keywords

weak Beth definabilityabstract model theorytwo-variable logichomogeneous model

MSC classification

Primary: 03C40: Interpolation, preservation, definability
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03C95: Abstract model theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 2 , June 2021 , pp. 785 - 800
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Copyright
© The Association for Symbolic Logic 2021

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