Hilbert's tenth problem for term algebras with a substitution operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00604240" target="_blank" >RIV/67985840:_____/24:00604240 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3233/COM-230444" target="_blank" >https://doi.org/10.3233/COM-230444</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3233/COM-230444" target="_blank" >10.3233/COM-230444</a>

Result language
angličtina
Original language name
Hilbert's tenth problem for term algebras with a substitution operator
Original language description
The analogue of Hilbert's 10th Problem for a first-order structure A with signature L asks whether there exists an algorithm that given an L-sentence of the form ∃ x → [ s = t ] decides whether ∃ x → [ s = t ] is true in A. In this paper, we consider term algebras over a finite signature with at least one constant symbol and one function symbol of arity at least two. We investigate the structure we obtain by extending the term algebra with a substitution operator. We prove undecidability of the analogue of Hilbert's 10th problem without relying on the solution to the original Hilbert's 10th Problem.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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