Deze serie publiceert substantiële, hoogwaardige werken op het gebied van de logica. Het overbrugt de kloof tussen inleidende doctoraatslezingen en gespecialiseerde onderzoeksmonografieën, en biedt nieuw materiaal dat nog niet eerder in boekvorm beschikbaar was. Elk deel biedt verhelderende perspectieven op diverse gebieden en aspecten van de logica voor een breed academisch publiek.
Focusing on admissible sets, this volume provides a clear and accessible introduction for both logic students and specialists. It breaks down complex concepts into fundamental facts, making it easier to understand this critical area of study in logic. The text serves as a valuable resource for those looking to enhance their knowledge and grasp the intricacies of admissible sets.
Focusing on first order stability theory, the book delves into the spectrum problem and provides comprehensive proofs of the Vaught conjecture specifically for ω-stable theories. It presents a structured approach to understanding these complex concepts, making it a valuable resource for those studying mathematical logic and model theory.
Stability theory began in the early 1960s with the work of Michael Morley and matured in the 70s through Shelah's research in model-theoretic classification theory. Today stability theory both influences and is influenced by number theory, algebraic group theory, Riemann surfaces and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. The aim of this book is to provide the student with a quick route from basic model theory to research in stability theory, to prepare a student for research in any of today's branches of stability theory and to give an introduction to classification theory with an exposition of Morley's Categoricity Theorem.
This book is an original contribution to the foundations of mathematics, with emphasis on the role of set existence axioms. Part A demonstrates that many familiar theorems of algebra, analysis, functional analysis,and combinatorics are logically equivalent to the axioms needed to prove them. This phenomenon is known as Reverse Mathematics. Subsystems of second order arithmetic based on such axioms correspond to several well known foundational programs: finitistic reductionism (Hilbert), constructivism (Bishop), predicativism (Weyl), and predicative reductionism (Feferman/Friedman). Part B is a thorough study of models of these and other systems. The book includes an extensive bibliography and a detailed index.