Let L be a countable first-order language and M = (M, . . .) be an L-structure. “Definable set” means a subset of M which is L-definable in M with parameters. A set X ⊆ M is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, A∩X is immune. X is said to be totally non-immune if for every definable A, A...

This paper gives an overview and an analysis of representative vowel space depictions found in the phonetic literature of the past four centuries. A visual representation of 24 selected structural proposals with time is given in poster form, after translation to a common notation. A first-order approach is developed by which the distance between any pair of vowel schemes may be measured. Using ...

The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the No-stable case which share many of the formal properties of fo...

The paper has a form of a survey on basics of logical geometry and consists of three parts. It is focused on the relationship between many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on important model-theoretic concepts. Our aim is to show that both approaches go in parallel and there are bridges which allow to transfer results, notions and problems bac...

We here present a sufficient condition for general arrowing problems to be non definable in first order logic, based in well known tools of finite model theory e.g. Hanf’s Theorem and known concepts in finite combinatorics, like senders and determiners.

In this paper we report on the formalization of the Tietze extension theorem using the MIZAR system. This theorem has been formalized as a part of the project aimed at formalizing the Jordan curve theorem. However, this development has turned out to be also useful for other formalizations.