This book describes a program of research in computable structure theory. The goal is to
find definability conditions corresponding to bounds on complexity which persist under …

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson,
Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory …

This book describes the latest Russian research covering the structure and algorithmic
properties of Boolean algebras from the algebraic and model-theoretic points of view. A …

We give a systematic technical exposition of the foundations of the theory of computably
compact metric spaces. We discover several new characterizations of computable …

Publisher Summary This chapter discusses the computability theory or recursion theory with
attempts to understand the algorithmic nature of the universe; combinatorics particularly …

We study computable Polish spaces and Polish groups up to homeomorphism. We prove a
natural effective analogy of Stone duality, and we also develop an effective definability …

Fried and Kollár constructed a fully faithful functor from the category of graphs to the
category of fields. We give a new construction of such a functor and use it to resolve a …

In mathematics, we know there are some concepts-objects, constructions, structures, proofs-
that are more complex and difficult to describe than others. Computable structure theory …

3. Theories, types, models, and diagrams. 138 4. Small theories and their models. 144 5.
Effective categoricity. 148 6. Automorphisms of effective structures. 156 7. Degree spectra of …

Feiner [F] showed that a Boolean algebra need not have a computable copy (see also [T2]).
Downey and Jockusch [DJ] showed that every low Boolean algebra does have a …