Infinitary stability theory

Infinitary stability theory

We introduce a new device in the study of abstract elementary classes (AECs): Galois Morleyization, which consists in expanding the models of the class with a relation for every Galois (orbital) type of length less than a fixed cardinal κ. We show: Theorem 0.1 (The semantic-syntactic correspondence). An AEC K is fully (< κ)-tame and type short if and only if Galois types are syntactic in the Ga...

Lectures on Infinitary Model Theory

Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in 40 years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, m...

Infinitary Rewriting--Theory and Applications

Infinitary rewriting generalises usual finitary rewriting by providing infinite reduction sequences with a notion of convergence. The idea of – at least conceptually – assigning a meaning to infinite derivations is well-known, for example, from lazy functional programming or from process calculi. Infinitary rewriting makes it possible to apply rewriting in order to obtain a formal model for suc...

Infinitary Proof Theory: the Multiplicative Additive Case

7 Infinitary and regular proofs are commonly used in fixed point logics. Being natural intermediate 8 devices between semantics and traditional finitary proof systems, they are commonly found in 9 completeness arguments, automated deduction, verification, etc. However, their proof theory 10 is surprisingly underdeveloped. In particular, very little is known about the computational 11 behavior o...

Infinitary Methods in Finite Model Theory