When we set out to write this book in the spring of 2011, the only introduction to reverse
mathematics was Simpson's Subsystems of Second Order Arithmetic [288]. Our motivation …

We investigate the problem of punctual (fully primitive recursive) presentability of algebraic
structures up to primitive recursive and computable isomorphism. We show that for mono …

We combine computable structure theory and algorithmic learning theory to study learning of
families of algebraic structures. Our main result is a model-theoretic characterization of the …

This paper is about naturally occurring objects in computability theory, the area inside
mathematical logic that studies the complexity of infinite countable objects. It is about the …

The present work consists of two separate investigations into the quantitative measurement
of the complexity of performing some computational task. In the first chapter, the task is …

We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by the
Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in …

The paper studies learnability from positive data for families of down-sets in quasi-orders,
and for families of ideals in Boolean algebras. We establish some connections between …

In the framework of Stewart Shapiro, computations are performed directly on strings of
symbols (numerals) whose abstract numerical interpretation is determined by a notation …

An\'etale structure over a topological space $ X $ is a continuous family of structures (in
some first-order language) indexed over $ X $. We give an exposition of this fundamental …

We investigate the interplay between the degree spectrum of a computable relation R on the
computable structure (ω,<), ie, natural numbers with the standard order, and the …