Epimorphisms, Definability and Cardinalities

0503853 - ÚI 2021 RIV NL eng J - Článek v odborném periodiku
Moraschini, Tommaso - Raftery, J.G. - Wannenburg, J. J.
Epimorphisms, Definability and Cardinalities.
Studia Logica. Roč. 108, č. 2 (2020), s. 255-275. ISSN 0039-3215. E-ISSN 1572-8730
Grant CEP: GA ČR GA17-04630S
GRANT EU: European Commission(XE) 689176 - SYSMICS
Institucionální podpora: RVO:67985807
Klíčová slova: Epimorphism * Prevariety * Quasivariety * Beth definability * Algebraizable logic * Equivalential logic
Obor OECD: Pure mathematics
Impakt faktor: 0.585, rok: 2020
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1007/s11225-019-09846-5

We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most s nonlogical symbols and an axiomatization requiring at most m variables, if the epimorphisms into structures with at most m + s + ℵ0 elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable 'bridge theorems', matching the surjectivity of all epimorphisms in the algebraic counterpart of a logic ⊢ with suitable infinitary definability properties of ⊢ , while not making the standard but awkward assumption that ⊢ comes furnished with a proper class of variables.
Trvalý link: http://hdl.handle.net/11104/0295628