Preliminaries to Classical First Order Model Theory

Preliminaries to Classical First Order Model Theory 1

First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretat...

Formalizing Basic First Order Model Theory

Basic first-order model theory in Mizar

The author has submitted to Mizar Mathematical Library a series of five articles introducing a framework for the formalization of classical first-order model theory. In them, Gödel’s completeness and Lowenheim-Skolem theorems have also been formalized for the countable case, to offer a first application of it and to showcase its utility. This is an overview and commentary on some key aspects of...

First-Order Classical Modal Logic

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness...

A Classical First Order Language

The aim is to construct a language for the classical predicate calculus. The language is defined as a subset of the language constructed in [7]. Well-formed formulas of this language are defined and some usual connectives and quantifiers of [7], [1] are accordingly. We prove inductive and definitional schemes for formulas of our language. Substitution for individual variables in formulas of the...