Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T₁, T₂ intersecting in a totally categorical sub-theory T₀. We show that if, e.g., T₀ is the theory of infinite vector spaces over a finite field then the fusion theory Tω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of Tω, proving that if both T₁, T₂ are 1-based then, Tω can be collapsed into a strongly minimal theory, if some (...) additional technical conditions hold—all trivially satisfied if T₀ is the theory of infinite vector spaces over a finite field Fq. (shrink)

We extend the construction of bad fields of characteristic zero to the case of arbitrary prescribed divisible green torsion.

The aim of this book is to present mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum. The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic: (...) first order logic and formal proofs, model theory, recursion theory, Gödel's incompleteness theorem, and, finally, the axiomatic set theory. Each chapter includes several interesting highlights—outside of logic when possible—either in the main text, or as exercises or appendices. Exercises are an essential component of the book, and a good number of them are designed to provide an opening to additional topics of interest. (shrink)

We study countable universes similar to a free action of a group G. It turns out that this is equivalent to the study of free semi-actions of G, with two universes being transformable iff one corresponding free semi-action can be obtained from the other by a finite alteration. In the case of a free group G (in finitely many or countably many generators), a classification is given.

We exhibit a theory where definable types lack the amalgamation property.