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         Logic Mathematical:     more books (100)
  1. Mathematical Logic by Stephen Cole Kleene, 2002-12-18
  2. My Best Mathematical and Logic Puzzles (Math & Logic Puzzles) by Martin Gardner, 1994-11-01
  3. A Mathematical Introduction to Logic, Second Edition by Herbert Enderton, Herbert B. Enderton, 2001-01-05
  4. A Course on Mathematical Logic (Universitext) by Shashi Mohan Srivastava, 2008-03-12
  5. Introduction to Logic by Alfred Tarski, 1995-03-27
  6. Introduction to Mathematical Logic, Fifth Edition (Discrete Mathematics and Its Applications) by Elliott Mendelson, 2009-08-11
  7. Proofs and Refutations: The Logic of Mathematical Discovery
  8. Fundamentals of Mathematical Logic by Peter G. Hinman, 2005-11-15
  9. Yes--No, Stop--Go: Some Patterns in Mathematical Logic (Young Math Books) by Judith L. Gersting, Joseph E. Kuczkowski, et all 1977-10
  10. Logic For Dummies by Mark Zegarelli, 2006-11-29
  11. A Profile of Mathematical Logic (Dover Books on Mathematics) by Howard DeLong, 2004-06-17
  12. A Concise Introduction to Mathematical Logic (Universitext) by Wolfgang Rautenberg, 2009-12-17
  13. Mathematical Logic by Joseph R. Shoenfield, 2001-01-15
  14. Mathematical Logic: A First Course (Dover Books on Mathematics) by Joel W. Robbin, 2006-07-07

1. Mathematical Logic - Wikipedia, The Free Encyclopedia
Mathematical logic is a subfield of logic and mathematics. 1 It consists both of the mathematical study of logic and the application of this study to
Mathematical logic
From Wikipedia, the free encyclopedia
Jump to: navigation search Mathematical logic is a subfield of logic and mathematics It consists both of the mathematical study of logic and the application of this study to other areas of mathematics. Mathematical logic has close connections to computer science and philosophical logic , as well. Unifying themes in mathematical logic include the expressive power of formal logics and the deductive power of formal proof systems. Since its inception, mathematical logic has contributed to, and has been motivated by, the study of foundations of mathematics . This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert 's program to prove the consistency of foundational theories. Results of Kurt G¶del Gerhard Gentzen , and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems , rather than trying to find theories in which all of mathematics can be developed.

2. Mathematical Logic
Mathematical logic was the inspiration for perhaps only half of twentiethcentury philosohpy (that is, of honest philosophy; by volume, as Kolakowski says,
Mathematical Logic
08 Sep 2004 11:07 If, in 1901, a talented and sympathetic outsider had been called upon (say, by a granting-giving agency) to survey the sciences and name the branch which would be least fruitful in century ahead, his choice might well have settled upon mathematical logic, an exceedingly recondite field whose practitioners could all have fit into a small auditorium - algebraists consumed by abstractive passion, or philosophers pursuing fantasies out of Leibniz and Ramon Llull, or (like Whitehead ) both. It had no practical applications, and not even that much mathematics to show for itself: its crown was an exceedingly obscure definition of cardinal numbers. When, in 1910, it produced a work which the learned world was forced to notice - the first volume of Whitehead and Russell 's Principia Mathematica - it was, so to speak, the academic Brief History of Time of its day, often mentioned, never used. Our outsider would, of course, have been wrong. Mathematical logic was the inspiration for perhaps only half of twentieth-century philosohpy (that is, of honest philosophy; by volume, as Kolakowski says, Stalin was the century's most influential philosopher); many of our finest mathematicians, such as

3. LPSG Mathematical Logic
Mathematical logic is about general properties of these formalizations. More specifically, it is about deduction and consistency, about models,
Last Updated 28/04/05 BACK TO LPSG CONTENTS
  • The Paper Textbooks
  • 1. The Paper
    The paper covers formal methods and results relevant to the philosophy of mathematics and philosophy of logic. It forms a natural pair with the Philosophy of Mathematics paper; each informs the other, but neither depends on the other. Most theories worthy of the name can be formalized. Mathematical logic is about general properties of these formalizations. More specifically, it is about deduction and consistency, about models, truth and consequence, about computability and axiomatizability. Mathematical logic will give one a firm grasp of concepts that are vital for philosopical logic and helpful in philosophy of language: truth, validity, consequence. In a first year introduction to logic, one learns deductive systems for propositional and first order predicate logic. But how do we know that these systems permit us to deduce only what is logically valid (soundness) and all of what is logically valid (completeness)? This course gives the answers. On the way, it presents basic reasoning techniques and basic semantic concepts: interpretation, satisfaction, truth under an interpretation, model. The paper is relatively demanding of one's mathematical abilities, but you do not have to be mathematically learned or clever. Success in the first year Introductory Logic course is pre-requisite. Mathematical logic, as all other mathematical subjects, is not a spectator sport; one must do the problems, as well go through the lecture notes (or textbook) to make sure you understand what is going on, after each lecture. If you keep up with this you are likely to do well in the exam.

    4. Mathematical Logic — Pioneers Of Bulgarian Mathematics
    Mathematical logic. Organizers. Dimiter Skordev. Valentin Goranko. Please log in to register for this section. Participants. Alexandra Andreeva Soskova

    5. Mathematical Logic - Definition From The Merriam-Webster Online Dictionary
    Definition of mathematical logic from the MerriamWebster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. logic
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    6. 03: Mathematical Logic And Foundations
    From The mathematical Atlas, a resource of mathematics maintained by David Rusin. Extensive resources related to logic and set theory.
    Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
    POINTERS: Texts Software Web links Selected topics here
    03: Mathematical logic and foundations
    Mathematical Logic is the study of the processes used in mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosophy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to Proof Theory. Students encounter elementary (sentential) logic early in their mathematical training. This includes techniques using truth tables, symbolic logic with only "and", "or", and "not" in the language, and various equivalences among methods of proof (e.g. proof by contradiction is a proof of the contrapositive). This material includes somewhat deeper results such as the existence of disjunctive normal forms for statements. Also fairly straightforward is elementary first-order logic, which adds quantifiers ("for all" and "there exists") to the language. The corresponding normal form is prenex normal form. In second-order logic, the quantifiers are allowed to apply to relations and functions to subsets as well as elements of a set. (For example, the well-ordering axiom of the integers is a second-order statement). So how can we characterize the set of theorems for the theory? The theorems are defined in a purely procedural way, yet they should be related to those statements which are (semantically) "true", that is, statements which are valid in every model of those axioms. With a suitable (and reasonably natural) set of rules of inference, the two notions coincide for any theory in first-order logic: the Soundness Theorem assures that what is provable is true, and the Completeness Theorem assures that what is true is provable. It follows that the set of true first-order statements is effectively enumerable, and decidable: one can deduce in a finite number of steps whether or not such a statement follows from the axioms. So, for example, one could make a countable list of all statements which are true for all groups.

    7. Mathematical Logic. Introduction. By V.Detlovs And K.Podnieks
    100% of a hypertextbook for students. Extended translation of V.Detlovs, Elements of mathematical logic, Riga, University of Latvia, 1964, 252 pp.
    mathematical logic, tutorial, what is logic, logic, mathematical, online, hyper-text, web, book, textbook, teaching, learning, study, student, Podnieks, Karlis, Detlovs, Vilnis, introduction, students, hypertext, text, hyper, free, download Doc. emeritus Vilnis Detlovs , 83, passed away on January 22, 2007.
    Born on May 26, 1923, he is best known for his 1950's proof of the equivalence of recursive functions and Markov's normal algorithms.
    See Memorial Page (in Latvian) Latviski Po-russki LU studentiem New! Lecture slides: The nature of mathematics (Sankt-Peterburg, June 22, 2006, in Russian)
    New! Lecture slides: What is science? Science is modeling! (Riga, February 8, 2007, in Latvian, English translation Personal page - click here This web-site presents a free hyper-textbook for students.
    My favorite (printed) textbook on mathematical logic, since many years:
    " Introduction to Mathematical Logic ", by Elliott Mendelson
    Introduction to Mathematical Logic
    Hyper-textbook for students
    by Vilnis Detlovs , Dr. math.

    8. Mathematical Logic Around The World
    Research groups, journals, organizations, conferences etc. in mathematical logic (such as set theory). By the mathematical logic Group, Bonn and the Vienna
    This page has (temporarily?) moved, to

    9. Mathematical Background
    Elementary or naive set theory is used to define basic mathematical structures Final Draft International Standard for Common logic. Mathematics WWW
    Mathematical Background
    by John F. Sowa This web page is a revised and extended version of Appendix A from the book Conceptual Structures by John F. Sowa. It presents a brief summary of the following topics for students and general readers of that book and related books such as Knowledge Representation and books on logic, linguistics, and computer science.
  • Sets, Bags, and Sequences
  • Functions
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  • References Note: Special symbols in this file that are outside the Latin-1 character set (ISO 8859-1) are represented by a .gif image for each character. The alt tag for each image gives the name of the character. Students who are just learning the symbols can move the mouse to any symbol to get a brief reminder of its name.
    1. Sets, Bags, and Sequences
    Elementary or "naive" set theory is used to define basic mathematical structures. A set is an arbitrary collection of elements, which may be real or imaginary, physical or abstract. In mathematics, sets are usually composed of abstract things like numbers and points, but one can also talk about sets of apples, oranges, people, or canaries. In computer science, sets are composed of bits, bytes, pointers, and blocks of storage. In many applications, the elements are never defined, but are left as abstractions that could be represented in many different ways in the human brain, on a piece of paper, or in computer storage. Curly braces are used to enclose a set specification. For small, finite sets, the specification of a set can be an exhaustive list of all its elements:
  • 10. Mathematical Logic Around The World
    A service provided by the mathematical logic Group in Bonn.
    Mathematical Logic around the world
    According to Google , this is one of the most authoritative sources for mathematical logic on the web. Please help building the logic network. Send us links and add a link on your page:
    <A HREF="">Mathematical Logic around the world</A>

    11. Simpson Math 557 Mathematical Logic
    Math 557 is an introductory graduatelevel course on mathematical logic. It is suitable for all mathematics graduate students. It is part of our first-year

    12. Archive For Mathematical Logic - Mathematical Logic And Foundations Journals, Bo
    Archive for mathematical logic Mathematics. The journal publishes research papers and occasionally surveys or expositions on mathematical logic.

    13. Bonn Mathematical Logic Group
    mathematical logic Group at the University of Bonn.
    Workgroup Prof. Peter Koepke
    home members research teaching ... information for prospective students
    Naproche Internship The Naproche project is offering one or two summer internships for May to July 2008. Further information on the Naproche site Young researchers in set theory workshop in Haus Annaberg. Starting at 9:00 o'clock on Monday, January 21going until Friday, January 25. more...
    to the Mathematical Logic Group at the University of Bonn. Our research areas are set theory and general logic. Please browse our website for details. Peter Koepke
    Mathematical logic
    Mathematical logic deals with the language of mathematics as well as the mathematics of language . Mathematical statements and arguments can be formulated in formal languages and calculi; formal languages possess mathematical properties. Traditionally, mathematical logic is subdivided into proof theory, model theory, set theory, and computability theory. more ...
    The research of the mathematical logic group is centered around the following topics:
    • Set Theory: models of set theory, combinatorics

    14. Wiley-VCH - MLQ - Mathematical Logic Quarterly
    mathematical logic Quarterly (MLQ) is an international journal for the publication of original research papers on mathematical logic, foundations of
    Journals Journals from A to Z MLQ - Mathematical Logic Quarterly Books Journals Please specify Architecture Biomedical Engineering Business Chemistry Civil Engineering Computer Science Earth Science Education Electrical Engineering Geography Graphics Design History Industrial Engin. Life Sciences Materials Science Mathematics Mechanical Engin. Medical Sciences Physics Social Science Statistics Journals from
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    ... Electronic Media Please specify Accounting Architecture Business Chemistry Civil Engineering Computer Certification Computer Science Earth Science Economics Education Electrical Engineering End-User Computing Finance Geography Graphics Design History Hospitality Industrial Engin. Law Life Sciences Lifestyles Materials Science Mathematics Mechanical Engin. Medical Sciences Physics Psychology Reference Religion Self-Help Social Science Statistics Travel MLQ - Mathematical Logic Quarterly
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    A Journal for Mathematical Logic, Foundations of Mathematics, and Logical Aspects of Theoretical Computer Science
    Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.

    15. ScienceDirect - Annals Of Mathematical Logic, Volume 23, Issues 2-3, Pages 101-2
    Annals of mathematical logic Copyright © 2007 Elsevier B.V. All rights reserved Continued as Annals of Pure and Applied logic
    Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Annals of Mathematical Logic
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    Publication History
    Continued as Annals of Pure and Applied Logic
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    Volume 23 (1982) Volume 23, Issues 2-3
    pp. 101-283 (December 1982) Volume 23, Issue 1
    pp. 1-99 (October 1982) Volume 22 (1982) Volume 21 (1981) Volume 20 (1981) Volume 19 (1980) ... Volume 1 (1970) Volume 23, Issues 2-3, Pages 101-283 (December 1982) No next vol/iss Article List Full Abstracts articles real singleton
    Pages 101-120
    Abstract + References PDF (1023 K) To Purchase and Download the Full Article , Click PDF View Related Articles reals Pages 121-125 Abstract Abstract + References PDF (220 K) To Purchase and Download the Full Article , Click PDF View Related Articles Recursive models for constructive set theories Pages 127-178 M. Beeson

    16. A Problem Course In Mathematical Logic
    Volume I Propositional and FirstOrder logic. Volume II Computability and Incompleteness.
    A Problem Course
    Mathematical Logic
    ... is a freeware mathematics text by Stefan Bilaniuk Current Release: Version 1.6 Released under the GNU Free Documentation License , Version 1.2 or later. Description Availability Conditions History ... Contacting the author
    A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method. The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory. Parts I and II

    17. Mathematics Archives - Topics In Mathematics - Logic & Set Theory
    KEYWORDS Plot functions, Solve a Diophantine Equation, Modulo arithmetic practice, Truth Table Practice, Symbolic logic; A Problem Course in mathematical
    Topics in Mathematics

    18. Group In Logic And The Methodology Of Science -
    Students in this program acquire a good understanding of the mathematical theory known as mathematical logic, which deals in a rigorous way with such
    Typical fields of study include
    • foundations of mathematics, including set theory, recursion theory, model theory, and theory of proofs, philosophical logic, including modal logic, philosophy of mathematics, logic in computer science and artificial intelligence, theory of computational complexity, history of logic,
    as well as other areas of research with heavy reliance on formal methods, such as general algebra, non-standard analysis, philosophy of language, and philosophy of science. Ph.D. work in logic can also be carried out entirely within one of the departments of Mathematics, Philosophy, Electrical Engineering and Computer Sciences (see Graduate Study in Logic at UC Berkeley ). The program in Logic and the Methodology of Science is intended for students whose interests lie in more than one of these fields. It offers them the possibility of taking qualifying examinations in more than one of these subjects; indeed, they must do so. Dissertations in this program may be interdisciplinary in character; however, they may also lie entirely within just one of these fields. The program is administered by the Group in Logic and the Methodology of Science, an interdepartmental agency which cooperates closely with the Department of Mathematics, the Department of Philosophy, and the Department of Electrical Engineering and Computer Sciences. The Group Office is located in 731 Evans Hall.

    19. BUBL LINK: Mathematical Logic
    Resource type journal; mathematical logic Around the World Links to sources of Author Modern logic Publishing Subjects mathematical logic
    BUBL LINK Catalogue of Internet Resources Home Search Subject Menus Countries ... Z
    Mathematical logic
    Titles Descriptions
  • Boole: Calculus of Logic Electronic Stacks Project Glossary of First-Order Logic Journal of Logic and Computation ... Modern Logic
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    Boole: Calculus of Logic
    An article by George Boole concerning propositional calculus, first published in Cambridge and Dublin Mathematical Journal Vol. III (1848). The article is available in HTML, LaTeX, DVI, and PostScript formats.
    Subjects: calculus, mathematical logic
    Resource type: article
    Electronic Stacks Project
    Project aiming to establish a distributed, evolving and live electronic dictionary of logic, an interdisciplinary subject covering philosophy, mathematics, language, psychology, computer science and artificial intelligence.
    Author: King's College London
    Subjects: mathematical logic, philosophical logic
    Resource type: documents
    Glossary of First-Order Logic
    Alphabetical list of terms relating to basic set theory, basic recursive function theory, truth-functional propositional logic and first-order predicate logic.
    Author: Suber, Peter

    20. Laboratory Of Mathematical Logic Of Steklov Institute Of Mathematics At St.Peter
    Laboratory of mathematical logic of the Steklov Institute of Mathematics.
    St. Petersburg Department of the Steklov Mathematical Institute
    Laboratory of Mathematical Logic
    [News] Staff Activities Seminars Hilbert's Tenth ... Staff Our activities Seminars Hilbert's Tenth Problem Relevant links
    • In the fall of '07 we have started the Computer Science Club that aims at providing students with advanced lectures on computer science.

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