A new proof of Ajtai's completeness theorem for nonstandard finite structures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317970" target="_blank" >RIV/00216208:11320/15:10317970 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00153-014-0416-5" target="_blank" >http://dx.doi.org/10.1007/s00153-014-0416-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-014-0416-5" target="_blank" >10.1007/s00153-014-0416-5</a>

Result language
angličtina
Original language name
A new proof of Ajtai's completeness theorem for nonstandard finite structures
Original language description
Ajtai's completeness theorem roughly states that a countable structure A coded in a model of arithmetic can be end-extended and expanded to a model of a given theory G if and only if a contradiction cannot be derived by a (possibly nonstandard) proof from G plus the diagram of A, provided that the proof is definable in A and contains only formulas of a standard length. The existence of such model extensions is closely related to questions in complexity theory. In this paper we give a new proof of Ajtai's theorem using basic techniques of model theory.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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