A Note on Natural Extensions in Abstract Algebraic Logic

0436388 - ÚI 2016 RIV NL eng J - Journal Article
Cintula, Petr - Noguera, Carles
A Note on Natural Extensions in Abstract Algebraic Logic.
Studia Logica. Roč. 103, č. 4 (2015), s. 815-823. ISSN 0039-3215. E-ISSN 1572-8730
R&D Projects: GA ČR(CZ) GA13-14654S
EU Projects: European Commission(XE) 247584 - MATOMUVI
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : abstract algebraic logic * consequence relations * natural extensions * transfer theorems
Subject RIV: BA - General Mathematics
Impact factor: 0.724, year: 2015

Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting (including all finitary logics and those with countable language) in which they can still be used.
Permanent Link: http://hdl.handle.net/11104/0240134