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

Pilar Dellunde, Àngel García-Cerdaña, Carles Noguera

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Abstract

© The Author 2016. This article is a contribution to the model theory of non-classical first-order predicate logics. In a wide framework of firstorder 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 two-sorted models.
Original languageEnglish
Article numberjzw009
Pages (from-to)321-345
JournalLogic Journal of the IGPL
Volume24
DOIs
Publication statusPublished - 20 Jun 2016

Keywords

  • Algebraizable logics
  • First-order predicate logics
  • Löwenheim-Skolem theorems
  • Model theory
  • Non-classical logics

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    Dellunde, P., García-Cerdaña, À., & Noguera, C. (2016). Löwenheim-Skolem theorems for non-classical first-order algebraizable logics. Logic Journal of the IGPL, 24, 321-345. [jzw009]. https://doi.org/10.1093/jigpal/jzw009