Löwenheim-Skolem theorems for non-classical first-order algebraizable logics

0469168 - ÚTIA 2017 RIV GB eng J - Journal Article
Dellunde, P. - García-Cerdaña, A. - Noguera, Carles
Löwenheim-Skolem theorems for non-classical first-order algebraizable logics.
Logic Journal of the IGPL. Roč. 24, č. 3 (2016), s. 321-345. ISSN 1367-0751. E-ISSN 1368-9894
R&D Projects: GA ČR GA13-14654S
Institutional support: RVO:67985556
Keywords : Löwenheim-Skolem theorems * first-order predicate logics * non-classical logics * algebraizable logics * model theory
Subject RIV: BA - General Mathematics
Impact factor: 0.575, year: 2016
http://library.utia.cas.cz/separaty/2016/MTR/noguera-0469168.pdf

This paper is a contribution to the model theory of non-classical first-order predicate logics. In a wide framework of first-order systems based on algebraizable logics, we study several notions of homomorphisms between models and find suitable definitions of elementary homomorphism, elementary substructure and elementary equivalence. Then we obtain (downward and upward) Löwenheim-Skolem theorems for these non-classical logics, by direct proofs and by describing their models as classical 2-sorted models.
Permanent Link: http://hdl.handle.net/11104/0269405