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 http://en.wikipedia.org/wiki/Mathematical_logic

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, http://www.cscs.umich.edu/~crshalizi/notabene/mathematical-logic.html

Notebooks 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, http://www.ucl.ac.uk/philosophy/LPSG/MathLogic.htm

MATHEMATICAL LOGIC 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 http://profot.fmi.uni-sofia.bg/sections/mathematics/mathematical-logic

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. http://www.merriam-webster.com/dictionary/mathematical logic

Home Visit Our Sites Unabridged Dictionary Learner's Dictionary ... Contact Us Also Visit: Unabridged Encyclopedia Britannica Visual ESL: Learner's for Kids: Spell It! Word Central Dictionary Thesaurus Spanish/English Medical Search "mathematical logic" in: Thesaurus Spanish/English Medical Dictionary Open Dictionary Browse words next to: mathematical logic Browse the Dictionary: A B C D ... Z mathematical logic One entry found. mathematical logic Main Entry: mathematical logic Function: noun Date: symbolic logic Learn more about "mathematical logic" and related topics at Britannica.com See a map of "mathematical logic" in the Visual Thesaurus Pronunciation Symbols Products Premium Services ... Advertising Info

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. http://www.math.niu.edu/~rusin/known-math/index/03-XX.html

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 Introduction 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. http://www.ltn.lv/~podnieks/mlog/ml.htm

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 http://www.uni-bonn.de/logic/world.html

This page has (temporarily?) moved, to http://world.logic.at

9. Mathematical Background Elementary or naive set theory is used to define basic mathematical structures Final Draft International Standard for Common logic. Mathematics WWW http://www.jfsowa.com/logic/math.htm

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 Lambda Calculus Graphs ... 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. http://world.logic.at/

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="http://world.logic.at">Mathematical Logic around the world</A> Logic Preprints and Journals Logic Groups Germany USA UK Elsewhere ... Other Links (including other lists of (not only) mathematical logic) Logic Preprints and Journals @ Los Alamos XXX Mathematics Archive AMS: MathSciNet Handbook of Set Theory Set Theory Preprint Sites (by author) Changes in "Set Theory Preprint Sites" , an automated blog keeping track of changes in the preprint webpages of some people working in set theory. CLE e-Prints (Centre for Logic, Epistemology and the History of Science at UNICAMP) Advanced Studies in Mathematics and Logic Algebra and Logic Algebra Universalis ... Postal addresses for logic journals Germany Aachen: Bonn: Dresden: Freiburg: Heidelberg: Kiel: Leipzig: Potsdam: Universität Potsdam USA California: Stanford UC Berkeley UC Irvine: Mathematics and Logic UCLA Delaware: University of Delaware Florida: University of Florida Illinois: UI at Urbana-Champaign UI at Chicago Indiana: Indiana University University of Notre Dame Massachusetts: MIT Michigan: University of Michigan Minnesota: University of Minnesota New Jersey: Rutgers University New York: Logic in the New York area Ohio: Ohio State University Pennsylvania: Carnegie Mellon University Pennsylvania State University University of Pennsylvania (Logic and Computation Group)

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 http://www.math.psu.edu/simpson/courses/math557/

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. http://www.springer.com/west/home/math?SGWID=4-10042-70-1012609-0

13. Bonn Mathematical Logic Group mathematical logic Group at the University of Bonn. http://www.math.uni-bonn.de/people/logic/

Workgroup Prof. Peter Koepke Menu home members research teaching ... information for prospective students News 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... Welcome 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 ... Research 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 http://www.wiley-vch.de/publish/en/journals/alphabeticIndex/2256/

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 A to Z Online Submission of Manuscripts ... 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 Latest Issue Access full text, free trials, sample copies, editorial and author information, news, and more. Bookmark 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 http://www.sciencedirect.com/science/journal/00034843

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 Shortcut URL to this page: http://www.sciencedirect.com/science/journal/00034843 Publication History Continued as Annals of Pure and Applied Logic Add to Favorites setCheckedBoxes ('/scidirimg/sci_dir', 'btn_apply1.gif', 'btn_apply1.gif'); About this Journal = Full-text available = Non-subscribed What does this mean? 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 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. http://euclid.trentu.ca/math/sb/pcml/

A Problem Course in 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 Description 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 http://archives.math.utk.edu/topics/logic.html

Topics in Mathematics The Alonzo Church Archive ADD. KEYWORDS: Manuscripts, Photographs AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases Around Goedel's theorem ADD. KEYWORDS: Textbook, Platonism, intuition and the nature of mathematics, Axiomatic set theory, First order arithmetic, Hilbert's Tenth problem, Incompleteness theorems, Around Goedel's theorem, About model theory Association for Symbolic Logic ADD. KEYWORDS: Society, Meetings Axiome du Choix ADD. KEYWORDS: Quelques variantes de l'axiome du choix. The Beginnings of Set Theory ADD. KEYWORDS: History, Cantor, Bolzano, Dedekind, Russell, Peano, Zermelo, Bibliography The Bulletin of Symbolic Logic ADD. KEYWORDS: Journal CMS Preprints: Set theory The Continuum Hypothesis ADD. KEYWORDS: Draft of an article A Crash Course in the Mathematics Of Infinite Sets ADD. KEYWORDS:

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 http://logic.berkeley.edu/

Home Faculty Officers Students ... Links Introduction 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 http://bubl.ac.uk/link/m/mathematicallogic.htm

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 Comments: bubl@bubl.ac.uk 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. Author: Subjects: calculus, mathematical logic DeweyClass: 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 DeweyClass: 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. http://logic.pdmi.ras.ru/

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 News 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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