Set theory

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

This introduction to mathematical logic takes Godel's incompleteness theorem as a starting point.

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences.

The study of polynomial completeness of algebraic systems has only recently matured, and until now, lacked a unified treatment.

This book presents and defends an original and paradigm-shifting conception of formal science, natural science, and the natural universe alike, that's fully pro-science, but at the same time neither theological or God-centered, nor solipsistic or self-centered, nor communitarian or social-institution-centered, nor scientistic or science-valorizing, nor materialist/physicalist or reductive, nor-above all-mechanistic.

Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices.

This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

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

Lateral Solutions to Mathematical Problems offers a fresh approach to mathematical problem solving via lateral thinking.

This textbook will continue to be the best suitable textbook written specifically for a first course on probability theory and designed for industrial engineering and operations management students.

This volume contains research papers in mathematical logic, particularly in model theory and its applications to algebra and formal theories of arithmetic.

This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis.

Quantum Computation presents the mathematics of quantum computation.

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.

This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture.

A deep dive into the historical and philosophical background of Gödel''s famed 1931 paper on incompleteness.

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 book deals with complexity, imprecision, human valuation, and uncertainty in spatial analysis and planning, providing a systematic exposure of a new philosophical and theoretical foundation for spatial analysis and planning under imprecision.

The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles.

For those who wonder if the forcing theory is beyond their means: no.

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members.

Solomon Feferman has shaped the field of foundational research for nearly half a century.

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

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members.

Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra.

This research level monograph reflects the current state of the field and provides a reference for graduate students entering the field as well as for established researchers.

A collection of remarkable papers from various areas of mathematical logic, written by outstanding members of the field.

This two-volume work bridges the gap between introductory texts and the research literature.

Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century.

Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic.

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

Gaps and limits are two phenomena occuring in the Boolean algebra P(&ohgr;)/fin.

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

How should we think about the meaning of the words that make up our language?

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.

This English translation of the author's original work has been thoroughly revised, expanded and updated.

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint.

This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology.

Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable.

A Beginner's Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics.

This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities.

A conference on Nonstandard Methods and Applications in Mathematics (NS2002) was held in Pisa, Italy from June 12-16, 2002.

This two-volume set bridges the gap between introductory texts and the research literature.

This book has enjoyed considerable use and appreciation during its first four editions.

This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005.