Towards a general theory of lattice-valued models

0520206 - ÚI 2020 CL eng A - Abstrakt
Cintula, Petr
Towards a general theory of lattice-valued models.
XVIII SLALM 16-20 December, 2019. Concepción: Universidad de Concepción, 2019. s. 6-6
Institucionální podpora: RVO:67985807
http://slalmxviii.udec.cl/sites/default/files/webform/Ses-Mod-Todos_0.pdf

Many generalizations of the basic setting of model theory have been proposed over the years. One of the more radical departures from the classical picture was the manyvalued generalization of the interpretation of predicate symbols, where relations are conceived as functions that assign, to each tuple of elements of the domain, values from a set that contains more than just the two classical values true and false. There are at least three different origins of research on these structures: Booleanvalued models, continuous model theory, and semantics of predicate many-valued logics. There are many papers studying basic and advanced model-theoretic properties of these structures, mostly focused on particular approaches and sets of problems with different levels of generality and mathematical sophistication. However, the common trait of these approaches is the fact that the values form a lattice. In my talk I propose a particular framework which could serve as a background for a general theory of lattice-valued structures and illustrate its utility by (1) a detailed analysis of possible forms of Skolem and Herbrand theorems and their interplay with compactness/finitarity and witnessed model property (a crucial notion in our setting which trivializes in classical model theory) (2) proving an analog of the omitting types theorem, and (3) establishing essential undecidability of very weak arithmetical theory.

Trvalý link: http://hdl.handle.net/11104/0304892