Recursive functions and existentially closed structures

0524146 - MÚ 2021 RIV SG eng J - Článek v odborném periodiku
Jeřábek, Emil
Recursive functions and existentially closed structures.
Journal of Mathematical Logic. Roč. 20, č. 1 (2020), č. článku 2050002. ISSN 0219-0613. E-ISSN 1793-6691
Grant CEP: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985840
Klíčová slova: classification theory * relative interpretation * representability of recursive functions
Obor OECD: Pure mathematics
Impakt faktor: 0.840, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1142/S0219061320500026

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson's theory R. To this end, we borrow tools from model theory-specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of theories interpretable in existential theories in the process.
Trvalý link: http://hdl.handle.net/11104/0308510