Set theory

The model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields.

Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles.

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering.

Combinatory logic is a versatile field that is connected to philosophical, mathematical, and computational logic.

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction.

Computability theory originated with the seminal work of Godel, Church, Turing, Kleene and Post in the 1930s.

Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory.

The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis.

Computability theory originated with the seminal work of Godel, Church, Turing, Kleene and Post in the 1930s.

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Godel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory.

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers.

Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today.

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors.

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors.

This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject.

This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject.

This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory.

This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory.

A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems.

A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems.

The Art of Proving Binomial Identities accomplishes two goals: (1) It provides a unified treatment of the binomial coefficients, and (2) Brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients).

The Art of Proving Binomial Identities accomplishes two goals: (1) It provides a unified treatment of the binomial coefficients, and (2) Brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients).

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists.

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists.

This Festschrift includes papers presented to honour Solomon Feferman on his seventieth birthday, reflecting his broad interests and his approach to foundational research.

Explores connections between infinitary model theory and other branches of mathematical logic, with algebraic applications.

Explores connections between infinitary model theory and other branches of mathematical logic, with algebraic applications.

This book constructs an inner model with a Woodin cardinal and develops its fine structure theory using the theory of iteration trees.

Proceedings of the Association for Symbolic Logic meeting held in Helsinki, Finland, in 1990, containing eighteen papers by leading researchers.

This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

This book presents the theory of proper forcing and its relatives from the beginning.

A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

This book brings together several directions of work in model theory between the late 1950s and early 1980s.

The theory set out in this book results from the meeting of descriptive set theory and recursion theory.

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau''s separation theorem for analytic sets.

Proceedings of the conference ''Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel''s Legacy'', held in 1996.

Suitable for graduate students and researchers in set theory, this volume develops a method for constructing core models that have Woodin cardinals.

Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, covering classical topics of mathematical logic.

An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

Set theory can be considered a unifying theory for mathematics.

Set theory can be considered a unifying theory for mathematics.

The third in a series of four books presenting the seminal papers from the Caltech-UCLA ''Cabal Seminar''.

The third in a series of four books presenting the seminal papers from the Caltech-UCLA ''Cabal Seminar''.

The Banach–Tarski Paradox seems patently false.

The Banach–Tarski Paradox seems patently false.

This book brings the researcher up to date with recent applications of mathematical logic to number theory.

This book brings the researcher up to date with recent applications of mathematical logic to number theory.