The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture kn...

The subject of this paper is the part of finite model theory intimately related to the classical model theory. In the very beginning of our career in computer science, we attended a few lectures on database theory where databases were inconspicuously allowed to be infinite and then classical model-theoretical theorems were applied. The use of infinite databases aroused our suspicion and prompte...

Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this paper I shall propose the notion of`knowledge assimilation', the assimilation of new information into a knowledge base, as an alternative understanding of the way in which a knowledge base formulated in logic relates to ...

In these notes I will look at that part of ”pre-Morley’s theorem era” model theory that I feel is most relevant for the current trends in model theory. Some of the topics are not chosen because of the theorems but because of the methods behind the proofs. Only the surface of each topic chosen is scratched, for more see [CK] or [Ho]. When we attach some names of persons to theorems, we just indi...

Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obst...

This study is concerned with the prediction of particles’ velocity in a dilute turbulent gas-solidboundary layer flow using a fully Eulerian two-fluid model. The closures required for equationsdescribing the particulate phase are derived from the kinetic theory of granular flows. Gas phaseturbulence is modeled by one-equation model and solid phase turbulence by MLH theory. Resultsof one-way and...

Computability theory formalizes the intuitive concepts of computation and information content. Pure computability studies these notions and how they relate to definability in arithmetic and set theory. Applied computability examines other areas of mathematics through the lens of effective processes. Tools from computability can be used to give precise definitions of concepts such as randomness....

The purpose of this article is to give a general introduction to the basic ideas and techniques from model theory. I begin with some general remarks concerning model theory and its relationship with algebra. There follows a “mini-course” on first order languages, structures and basic ideas in model theory. Then there is a series of subsections which describe briefly some topics from model theory.