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Logic and Its Applications
Two conferences, Logic and Its Applications in Algebra and Geometry and Combinatorial Set Theory, Excellent Classes, and Schanuel Conjecture, were held at the University of Michigan (Ann Arbor). These events brought together model theorists and set theorists working in these areas. This volume is the result of those meetings. It is suitable for graduate students and researchers working in mathematical logic.
Models, Algebras, and Proofs
Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts.
Beyond First Order Model Theory, Volume II
A coherent introduction to current trends in model theory Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together Suitable as a reference for advanced undergraduate, postgraduates, and researchers Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature The various chapters in the book can be studied independently.
Mexican Mathematicians in the World
Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10–15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields.
Applications of Model Theory to Functional Analysis
The first self-contained introduction to techniques of model theory, this 2002 text presents material still not readily available elsewhere, including Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces.
Analysis and Logic
This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
Beyond First Order Model Theory, Volume I
Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.
Logica Universalis
Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic. It was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. The present book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. It will help those who are lost in the jungle of heterogeneous logical systems to find a way. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.
Geometric Aspects of Functional Analysis
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.
Topics In Model Theory
This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory,' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
