Mathematical Logic


Modal Logic (7)
Model Theory (8)
Proof Theory (9)
Set Theory (14)

see also

Computability Theory (8)

e-books in Mathematical Logic category

What is Mathematics: Gödel's Theorem and AroundWhat is Mathematics: Gödel's Theorem and Around
by Karlis Podnieks - University of Latvia , 2013
Textbook for students in mathematical logic and foundations of mathematics. Contents: Platonism, intuition and the nature of mathematics; Axiomatic Set Theory; First Order Arithmetic; Hilbert's Tenth Problem; Incompleteness Theorems; Godel's Theorem.
Introduction to Mathematical LogicIntroduction to Mathematical Logic
by Vilnis Detlovs, Karlis Podnieks - University of Latvia , 2014
From the table of contents: 1. Introduction. What Is Logic, Really?; 2. Propositional Logic; 3. Predicate Logic; 4. Completeness Theorems (Model Theory); 5. Normal Forms. Resolution Method; 6. Miscellaneous (Negation as Contradiction or Absurdity).
Logic for Computer ScienceLogic for Computer Science
- Wikibooks , 2010
This book provides a survey of mathematical logic and its various applications. After covering basic material of propositional logic and first-order logic, the course presents the foundations of finite model theory and descriptive complexity.
Natural TopologyNatural Topology
by Frank Waaldijk - arXiv , 2012
We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism.

Logic for Computer ScientistsLogic for Computer Scientists
by Uli Furbach - Wikibooks , 2010
This book is intended for computer scientists and it assumes only some basic mathematical notions like relations and orderings. The aim was to create an interactive script where logics can be experienced by interaction and experimentation.
Logics of Time and ComputationLogics of Time and Computation
by Robert Goldblatt - Center for the Study of Language , 1992
Sets out the basic theory of normal modal and temporal propositional logics, applies this theory to logics of discrete, dense, and continuous time, to the temporal logic of henceforth, next, and until, and to the dynamic logic of regular programs.
Intuitionistic LogicIntuitionistic Logic
by Nick Bezhanishvili, Dick de Jongh - Universiteit van Amsterdam , 2010
In this course we give an introduction to intuitionistic logic. We concentrate on the propositional calculus mostly, make some minor excursions to the predicate calculus and to the use of intuitionistic logic in intuitionistic formal systems.
A Manual of Intensional LogicA Manual of Intensional Logic
by Johan van Benthem - CSLI , 1988
An examination of the role of partial information - with illustrations drawn from different branches of Intensional Logic - and various influences stemming from current theories of the semantics of natural language, involving generalized quantifiers.
Lectures on Linear LogicLectures on Linear Logic
by A. S. Troelstra - CSLI , 1992
This text deals with logical formalism, cut-elimination, the embedding of intuitionistic logic in classical linear logic, proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
A Second Course in LogicA Second Course in Logic
by Christopher Gauker - University of Cincinnati , 2013
This book is for anyone who has had a solid introductory logic course and wants more. Topics covered include soundness and completeness for first-order logic, Tarski's theorem on the undefinability of truth, Godel's incompleteness theorems, etc.
Notes on the Science of LogicNotes on the Science of Logic
by Nuel Belnap - University of Pittsburgh , 2009
This course assumes you know how to use truth functions and quantifiers as tools. Our task here is to study these very tools. Contents: logic of truth functional connectives; first order logic of extensional predicates, operators, and quantifiers.
The Art of LogicThe Art of Logic
by Nuel Belnap - University of Pittsburgh , 2009
Contents: Grammar; The art of the logic of truth-functional connectives; Quantifier proofs; A modicum of set theory; Symbolizing English quantifiers; Quantifier semantics - interpretation and counterexample; Theories; Definitions.
An Introduction to Mathematical LogicAn Introduction to Mathematical Logic
by Wolfram Pohlers, Thomas Glass , 1992
This text treats pure logic and in this connection introduces to basic proof-theoretic techniques. Fundamentals of model theory and those of recursion theory are dealt with. Furthermore, some extensions of first order logic are treated.
Symbolic Logic: A Second CourseSymbolic Logic: A Second Course
by Gary Hardegree - UMass Amherst , 2003
Contents: Summary; Translations in Function Logic; Derivations in Function Logic; Translations in Identity Logic; Extra Material on Identity Logic; Derivations in Identity Logic; Translations in Description Logic; Derivations in Description Logic.
Symbolic Logic: A First CourseSymbolic Logic: A First Course
by Gary Hardegree - Mcgraw-Hill College , 1999
Contents: Basic Concepts of Logic; Truth-Functional Connectives; Validity in Sentential Logic; Translations in Sentential Logic; Derivations in Sentential Logic; Translations in Monadic Predicate Logic; Translations in Polyadic Predicate Logic; etc.
Algebraic LogicAlgebraic Logic
by H. Andreka, I. Nemeti, I. Sain , 2003
Part I of the book studies algebras which are relevant to logic. Part II deals with the methodology of solving logic problems by (i) translating them to algebra, (ii) solving the algebraic problem, and (iii) translating the result back to logic.
The Principles Of MathematicsThe Principles Of Mathematics
by Bertrand Russell - W. W. Norton & Company
Russell's classic sets forth his landmark thesis that mathematics and logic are identical -- that what is called mathematics is simply later deductions from logical premises. His ideas have had a profound influence on the foundations of mathematics.
A Concise Introduction to Mathematical LogicA Concise Introduction to Mathematical Logic
by Wolfgang Rautenberg - Springer , 2009
A well-written introduction to the beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Goedel's incompleteness theorems, as well as some topics motivated by applications.
Introduction to Mathematical Logic: A problem solving courseIntroduction to Mathematical Logic: A problem solving course
by Arnold W. Miller - arXiv , 1996
This is a set of questions written for a course in Mathematical Logic. Topics covered are: propositional logic; axioms of ZFC; wellorderings and equivalents of AC; ordinal and cardinal arithmetic; first order logic, and the compactness theorem; etc.
The Algebra of LogicThe Algebra of Logic
by Louis Couturat - Project Gutenberg , 2004
Mathematical Logic is a necessary preliminary to logical Mathematics. The present work is concerned with the 'calculus ratiocinator' aspect, and shows, in an admirably succinct form, the beauty of the calculus of logic regarded as an algebra.
The Haskell Road to Logic, Maths and ProgrammingThe Haskell Road to Logic, Maths and Programming
by Kees Doets, Jan van Eijck - College Publications , 2004
The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming. The programming language that will be our tool for this is Haskell, a member of the Lisp family.
Formal LogicFormal Logic
- Wikibooks , 2009
An undergraduate college level textbook covering first order predicate logic with identity but omitting metalogical proofs. The first rules of formal logic were written over 2300 years ago by Aristotle and are still vital.
Introduction to Mathematical PhilosophyIntroduction to Mathematical Philosophy
by Bertrand Russell - University of Massachusetts Amherst , 2009
A very accessible mathematical classic. It sets forth in elementary form the logical definition of number, the analysis of the notion of order, the modern doctrine of the infinite, and the theory of descriptions and classes as symbolic fictions.
Introduction to LogicIntroduction to Logic
by Michal Walicki - University of Bergen , 2006
This text is an introduction to mathematical logic: the compendium with the whole syllabus and an extensive section on the history of logic. The author covers the basic set theory, Turing machines, statement logic, and predicate logic.
Mathematical LogicMathematical Logic
by Stephen G. Simpson - Pennsylvania State University , 2013
Lecture notes for all mathematics graduate students. The text covers propositional calculus, predicate calculus, proof systems, extensions of the predicate calculus, theories, definability, interpretability, arithmetization and incompleteness.
Logic For EveryoneLogic For Everyone
by Robert A. Herrmann , 2006
This is Robert Herrmann's elementary book in mathematical logic that includes all basic material in the predicate and propositional calculus presented in a unique manner. Neither proof requires specialized mathematical procedures.
forall x: An Introduction to Formal Logicforall x: An Introduction to Formal Logic
by P.D. Magnus , 2008
An introduction to sentential logic and first-order predicate logic with identity, logical systems that influenced twentieth-century analytic philosophy. The book should help students understand quantified expressions in their philosophical reading.
Predicative ArithmeticPredicative Arithmetic
by Edward Nelson - Princeton Univ Pr , 1987
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
A Problem Course in Mathematical LogicA Problem Course in Mathematical Logic
by Stefan Bilaniuk , 2003
An introduction to mathematical logic for undergraduates. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is to learn the material by solving the problems.