61. Dana Scott's Home Page Carnegie Mellon University Model theory, set theory, foundations of logic and mathematics, symbolic mathematical computation. http://www.cs.cmu.edu/~scott/

Dana S. Scott Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic (Emeritus) Mailing Address: Prof. Dana S. Scott Office : N/A Computer Science Department Wean Hall Phone Carnegie Mellon University Pittsburgh, PA 15213-3890 , USA FAX : (412) 268-5576 (In CS Main Office) Home Address (Fall 2004): 401 Amberson Ave. Apt. 303 Phone Pittsburgh, PA, 15232, USA Secretary: Charlotte Yano (WeH 7121) Phone Travel: In California for Summer 2004 Personal: Career Highlights Ph.D. Students Current Research Teaching: E-MAIL: dana.scott@cs.cmu.edu yano@cs.cmu.edu Last revised: 24 May 2004

62. 1.1. Notation And Set Theory So far, we have reviewed a few basic facts from set theory, and also got an thosedefinitions we derive new results, based on old results, notation, and logic. http://www.shu.edu/projects/reals/logic/notation.html

1.1. Notation and Set Theory IRA Sets are the most basic building blocks in mathematics, and it is in fact not easy to give a precise definition of the mathematical object set . Once sets are introduced, however, one can compare them, define operations similar to addition and multiplication on them, and use them to define new objects such as various kinds of number systems. In fact, most of the topics in modern analysis are ultimately based on sets. Therefore, it is good to have a basic understanding of sets, and we will review a few elementary facts in this section. Most, if not all, of this section should be familiar and its main purpose is to define the basic notation so that there will be no confusion in the remainder of this text. Definition 1.1.1: Sets and Operations on Sets A set is a collection of objects chosen from some universe. The universe is usually understood from the context. Sets are denoted by capital, bold letters or curly brackets. A B A is a subset of B means that every element in A is also contained in B A B A union B is the set of all elements that are either in A or in B or in both.

63. Logic At Leeds - Homepage Mathematical logic Group. Research areas recursion theory, model theory, set theory and foundations, proof theory, and in applications to algebra, analysis and theoretical computer science. Members, events, seminars. http://www.amsta.leeds.ac.uk/Pure/logic/

People Research Seminars Postgrad opportunities Pure Department School of Mathematics University of Leeds Some outside links The Leeds Logic Group The group is one of the largest and most active in Europe, with an international reputation for research in several of the main areas of mathematical logic - computability theory, model theory, set theory and foundations, proof theory, and in applications to algebra, analysis and theoretical computer science. The group has been very successful in obtaining EPSRC and EU support for Research Students and Post-Doctoral Fellows, and has been the focus of extensive international collaboration via various research projects and networks in proof theory, computability theory and model theory. Our past postgraduates and researchers have been very successful in moving to research or teaching positions in Mathematics and Computer Science departments around the world. Further details of individual staff's research interests can be found on their homepages, accessed via the links on the left. Applications to visit or to pursue research within the Leeds Logic Group are always welcome. Please contact our postgraduate tutor, Prof. Dugald Macpherson for more information: NEWS The British Logic Colloquium 2004 , will be at the University of Leeds, September 6 - 8.

64. SCHOOL OF MATHEMATICS Department of Mathematics, logic Group. Research interests model theory, uncertain reasoning and logical aspects of AI, variants of classical set theory and their applications, and formalisation in theory and practice. Members, courses. http://www.maths.man.ac.uk/DeptWeb/Groups/Logic/LogicResearch.html

SCHOOL OF MATHEMATICS People Undergraduate Postgraduate Seminars ... External This page has moved, you should be redirected to its new location in 5 seconds. If you are not forwarded to the new page (or if you cannot wait 5 seconds!) click here

65. Modern Logic Home Page International Journal for the History of Mathematical logic, set theory, and Foundations of Mathematics. http://www.ed.ac.uk/~pmilne/ml/home.html

M ODERN L OGIC A Journal for the History, Philosophy, Invention, and Pedagogy of Modern Logic, Set Theory, and the Foundations of Mathematics ISSN 1047-5982 Mathematical logic...is the modern form of logic developed in the last hundred years. - Rudolf Carnap (1954) This site covers Volumes 1 to 8 of Modern Logic Starting with Volume 9, the journal is to continue as The Review of Modern Logic Contents Description and goals Editorial Board of Modern Logic Subscription and publication information ... Contents issue by issue with abstracts Modern Logic is currently abstracted in Bibliograficheskikh Ukazatelyakh Current Mathematical Publications Historia Mathematica Mathematical Reviews Referativnyi Zhurnal - Matematika Referativnyi Zhurnal - Filosofiya i Sotsiologiya Zentralblatt fuer Mathematik and the MathSci online database, and has exchange agreements with From the Logical Point of View Logique et Analyse LLULL: Revista de la Sociedad Espanola de Historia des las Ciencas y de las Tecnicas Manuscrito Mathesis Revue d'Histoire des Mathematiques Russell Studia Logica and Synthesis Philosophica/Filozofska Istrazivanja Modern Logic home page Description and goals Editorial Board of ... Contents issue by issue with abstracts

66. 6th Barcelona Logic Meeting 6th Barcelona logic Meeting, 58 July 2000 - Barcelona, Spain - Areas emphasized are algebraic logic, model theory and set theory. http://www.crm.es/pastactivities/Act1999-2000/6blm.htm

July 5 to 8, 2000 Programme (updated July 4) The Sixth Barcelona Logic Meeting will be held from Wednesday, July 5th to Saturday, July 8th, 2000 in the Institut d'Estudis Catalans, IEC , Carme 47, Barcelona (note that in previous announcements the dates were 6 to 8). The meeting will be devoted to all areas of Mathematical Logic, with an emphasis in Algebraic Logic, Model Theory and Set Theory. The scientific program will consist of several one-hour invited lectures and a number of twenty-minute contributed talks. The 6th BLM is financially supported by the European Union in its "Euroconferences" series, by the spanish Ministry of Science and Culture and by the University of Barcelona. It is administratively supported by the Centre de Recerca Matemàtica of the Institut d'Estudis Catalans. We are also expecting financial support from other Catalan universities and Catalan funding agencies. The 6th BLM has been recognized as a satellite conference of the 3rd European Congress of Mathematics, to be held in Barcelona, July 10-14, 2000 under the auspices of the European Mathematical Society. Scientific and Organizing Committee JOAN BAGARIA Universitat de Barcelona ENRIQUE CASANOVAS Universitat de Barcelona RAFEL FARRÉ Universitat Politècnica de Catalunya JOSEP MARIA FONT Universitat de Barcelona JUAN CARLOS MARTÍNEZ Universitat de Barcelona HIROAKIRA ONO Japan Advanced Institute of Science and Technology MARGARITA OTERO

67. Topic: Logic, Set Theory, And Algebra [ 0210-v ] Topic logic, set theory, and algebra Topics General, Mathematical methods inphysics, logic, set theory, and algebra, Your browser is not able to display http://topics.aip.org/0210-_FS.html

Topic: Logic, set theory, and algebra Topics: General, Mathematical methods in physics, Logic, set theory, and algebra

68. Set Theory And Logic - Numericana Final Answers © 20002004 Gérard P. Michon, Ph.D. set theory and logic.The Barber s Dilemma. set theory logic. (Ashlee of Braithwaite, LA. http://home.att.net/~numericana/answer/sets.htm

home index units counting ... physics Final Answers , Ph.D. Set Theory and Logic The Barber's Dilemma . Not a paradox if analyzed properly. What is infinity ? More than a pretty symbol ( There are more real than rational numbers . Cantor's argument. The axioms of set theory : Fundamental axioms and the Axiom of Choice Transfinite cardinals, transfinite ordinals : Two different kinds of infinite numbers Surreal Numbers more (Ashlee of Braithwaite, LA. twice There is a barber who lives in a small town. The barber shaves all those men and only those men who do not shave themselves. Does the barber shave himself? Stay away from the many "cute" answers that do not really address the question: The barber can't be a woman (otherwise the term "himself" used in the question would be improper). It would also be cheating to consider that the barber is a boy (and therefore not a "man") or any other kind of non-human male creature for that matter... The dilemma remains (it's not a paradadox, as we shall see): If the barber doesn't shave himself then he shaves himself. If he shaves himself, then he doesn't shave himself. The answer to this classic "problem" is simple: There cannot possibly be any such barber!

69. Russell's Paradox Discovered by Bertrand Russell in 1901, the paradox has prompted much workin logic, set theory and the philosophy and foundations of mathematics. http://plato.stanford.edu/entries/russell-paradox/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAY Russell's Paradox Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves " R ." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics. History of the paradox Significance of the paradox Bibliography Other Internet Resources ... Related Entries History of the paradox Russell appears to have discovered his paradox in the late spring of 1901

70. Set Theory, Logic, Probability Statistics - Technology Services Physics Help and Math Help Physics Forums Mathematics set theory,logic, Probability Statistics. View Statistics. Click Here. http://www.physicsforums.com/archive/f-78

Physics Help and Math Help - Physics Forums Mathematics View Forum : Need help with polynomial fitting Markov to compare matrices Godel and Inconsistency probability/statistics question help ... Car Body Parts Physics Forums is a network of science forums with an emphasis on physics help and star astronomy. Register to post your physics questions or just hang out and talk about general science topics!

71. Physics Help And Math Help - Physics Forums - Set Theory, Logic, Probability & S Reload this Page set theory, logic, Probability Statistics. User Name, RememberMe? Threads in Forum set theory, logic, Probability Statistics, Forum Tools. http://www.physicsforums.com/forumdisplay.php?f=78

72. Set Theory And Its Logic set theory and Its logic. set theory and Its logic by Authors Willard V. QuineReleased June, 1969 ISBN 0674802071 Paperback Sales Rank 278,833, http://www.phil-books.com/Set_Theory_and_Its_Logic_0674802071.html

Set Theory and Its Logic Set Theory and Its Logic by Authors: Willard V. Quine Released: June, 1969 ISBN: 0674802071 Paperback Sales Rank: List price: Our price: Book > Set Theory and Its Logic > Customer Reviews: Average Customer Rating: Set Theory and Its Logic > Customer Review #1: Excellent treatment. Id rather read Enderton, but this is a Quine classic. Not too helpful (the review, not the book), but mathematics reviews seldom are. As I say, Enderton, or Jech and Hrbacek. Set Theory and Its Logic > Related Products Mathematical Logic Elementary Logic Methods of Logic The Web of Belief ... phil - books

73. Earliest Uses Of Symbols Of Set Theory And Logic Earliest Uses of Symbols of set theory and logic. Last updated July 14,1999 Intersection and union. Giuseppe Peano (18581932) introduced http://mail.mcjh.kl.edu.tw/~chenkwn/mathword/set.html

Earliest Uses of Symbols of Set Theory and Logic Last updated: July 14, 1999 Intersection and union. Giuseppe Peano (1858-1932) introduced and in 1888 in Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann (Cajori vol. 2, page 298). According to Schwartzman (p. 118) the intersection symbol above dates back to Leibniz "who also used it to indicate regular multiplication." Cajori says Leibniz used the symbol for multiplication, but seems not to confirm that he used it for intersection. Existence. Peano used in volume II, number 1, of his which was published in 1897 (Cajori vol. 2, page 300). Membership. Peano used in the introduction to volume I of his which was published in Turin in 1895, although the introduction itself is dated 1894 (Cajori vol. 2, page 300). The website at the University of St. Andrews states that Peano introduced the symbol in 1889 and that it comes from the first letter if the Greek word meaning "is." Peano's symbol for membership was an ordinary epsilon ; the stylized epsilon now used was adopted by Bertrand Russell in Principles of Mathematics Such that.

74. Basics Of Fuzzy Logic And Fuzzy Set Theory Basics of Fuzzy logic and Fuzzy set theory. The concept of fuzzy setand fuzzy logic were introduced by Zadeh Zadeh, 1965. Zadeh http://www.ncst.ernet.in/kbcs/vivek/issues/11.1/sam/node2.html

Next: Neonatal Resuscitation Management: An Up: On Fuzzy Concepts in Previous: Introduction Basics of Fuzzy Logic and Fuzzy Set Theory for no membership; for full membership; for partial membership. Having obtained the numerical representation of these linguistic terms, one has to define the set theoretic operations of union, intersection and complementation along with their logical counterparts of conjunction, disjunction and complementation as follows: Union (logical OR)- the membership of an element in the union of two fuzzy sets is the larger of the memberships in these sets. (A OR B) = max((A), (B)) e.g., (tall OR small) = max((tall), (small)) Intersection (logical AND)- the membership of an element in the intersection of two fuzzy sets is the smaller of the memberships in these sets. (A AND B) = min((A), (B)) e.g., (tall AND small) = min((tall), (small)) Complement (logical NOT)- the degree of truth of the membership to the complement of the set is defined as (1 - membership). (NOT A) = 1 - (A) e.g., (NOT tall) = (1 - (tall))

75. Science, Math, Logic And Foundations: Set Theory A Crash Course in the Mathematics of Infinite sets A introductory guide forphilosophers by Peter Suber, explaining the use of infinitary set theory. http://www.combose.com/Science/Math/Logic_and_Foundations/Set_Theory/

Top Science Math Logic and Foundations ... A Crash Course in the Mathematics of Infinite Sets - A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory. Axiom of Choice and Continuum Hypothesis - Part of the Frequently Asked Questions in Mathematics. Bounded Set Theory - A weak version of ordinary set theory using bounded quantification. Papers and software. Cantor's Theorem - Article in the Platonic Realms, describing Cantor's diagonal argument that proved that infinity comes in many different 'sizes'. Consequences of the Axiom of Choice Project - Project to keep the book (also named in the title), describing forms related to the Axiom of Choice and their implications, updated. Equivalence Relation - Encyclopedia entry on equivalence relations and their role in set theory. Infinite Ink: The Continuum Hypothesis, by Nancy McGough - History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis Issues in Commonsense Set Theory - Paper by M¼jdat Pakkan and Varol Akman Metamath Proof Explorer - Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms.

76. Problems In Set Theory Mathematical Logic And The Theory Of Algorithms (Universi Problems in set theory Mathematical logic and the theory of Algorithms(University Series in Mathematics). Problems in set theory http://www.victorcunningham.co.uk/Problems-in-Set-Theory-Mathematical-Logic-and-

Problems in Set Theory Mathematical Logic and the Theory of Algorithms (University Series in Mathematics) Title: Problems in Set Theory Mathematical Logic and the Theory of Algorithms (University Series in Mathematics) Subject: Algorithms; Problems exercises etc Category: Science Nature Mathematics Mathematical Foundations Mathematical Logic Format: Hardcover Chris J. Dalglish-Rural Society in the Age of Reason: An Archaeology of the Emergence of Modern Life in the Southern Scottish Highlands (Contributions to Global Historical Archaeology)... The Genus Yersinia: Entering the Functional Genomic Era: Proceedings 8th International Symposium on Yersinia, Turku, Finland, on September 4-8, 2002 (Advances in Experimental Medicine and Biology)... Sivarama Dandamudi-Hierarchical Scheduling in Parallel and Cluster Systems (Series in Computer Science)... Chris J. Dalglish-Rural Society in the Age of Reason: An Archaeology of the Emergence of Modern Life in the Southern Scottish Highlands (Contributions to Global Historical Archaeology)... ... Dr Seuss-The Best of Dr. Seuss: The Cat in the Hat / the Cat in the Hat Comes Back / Dr Seuss's ABC...

77. Science Search > Set Theory 8. Bounded set theory A weak version of ordinary set theory using bounded quantification.Papers and software. http//www.botik.ru/~logic/bst/bst.html 06-10 http://www.science-search.org/index/Math/Logic_and_Foundations/Set_Theory/

Search for: Current Category Everything What's new Top Searches Statistics Science News ... Home Current location: Math Logic and Foundations > Set Theory The Beginnings of Set Theory MacTutor History of Mathematics topic. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html detailed information Rating: [7.00] Votes: [2242] Metamath Proof Explorer Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms. http://metamath.org detailed information Rating: [6.01] Votes: [383] A Crash Course in the Mathematics of Infinite Sets A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory. http://www.earlham.edu/~peters/writing/infapp.htm detailed information Rating: [6.00] Votes: [420] Set Theory Directory of set theorists, maintained by Jean A. Larson. http://www.math.ufl.edu/~jal/set_theory.html detailed information Rating: [6.00] Votes: [16] Set Theory Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.

78. Set Theory And Logic set theory and logic. set theory and logic by Authors Robert R. Stoll Released01 October, 1979 ISBN 0486638294 Paperback Sales Rank 78,946, http://www.sciencesbookreview.com/Set_Theory_and_Logic_0486638294.html

Set Theory and Logic Set Theory and Logic by Authors: Robert R. Stoll Released: 01 October, 1979 ISBN: 0486638294 Paperback Sales Rank: List price: Our price: You save: Book > Set Theory and Logic > Customer Reviews: Average Customer Rating: Set Theory and Logic > Customer Review #1: Incredible Best Buy This book is without peer in its breadth of coverage of the foundations of mathematics and logic. I have given this book only 4 stars, because its treatment of any given topic is not classic. It is the total package that astounds. For a mere $15, you get a challenging undergraduate introduction to all of the following topics. I have written in parentheses the names of authors of more definitive treatments: Intuitive set theory through the axiom of choice (Halmos) Natural numbers † Integers † Rationals † Reals (Feferman) Mathematical logic (Machover, Smullyan)

79. Set Theory, Logic And Their Limitations set theory, logic and their Limitations. List price $33.00 Our price $33.00.Book set theory, logic and their Limitations Customer Reviews http://www.sciencesbookreview.com/Set_Theory_Logic_and_their_Limitations_0521479

Set Theory, Logic and their Limitations Set Theory, Logic and their Limitations by Authors: Moshe Machover Released: 23 May, 1996 ISBN: 0521479983 Paperback Sales Rank: List price: Our price: Book > Set Theory, Logic and their Limitations > Customer Reviews: Average Customer Rating: Set Theory, Logic and their Limitations > Customer Review #1: Best treatment of propositional calculus I know This is an outstanding advanced undergraduate treatment of the following topics at the core of modern mathematics: set theory, equivalence and ordering relations, cardinals, ordinals, propositional logic, quantifier logic, and just enough recursion theory to explain the paradoxical undecidability theorems. The treatment is thoroughly contemporary (eg, Hintikka sets) but not too difficult, because this text emerged out of the philosophy rather than the mathematics classroom. The text is written in the mathematical tradition, consisting of many terse numbered subsections, each containing a definition, theorem, remark, or problem. The organisation of the subject, and the index, are excellent. This is the finest treatment I know of the propositional calculus, the core of modern logic and the subject that drew me to this book.

80. Harvard University Press/Set Theory And Its Logic, Revised Edition set theory and Its logic, Revised Edition by WV Quine, published by HarvardUniversity Press. set theory and Its logic, Revised Edition WV Quine. http://www.hup.harvard.edu/catalog/QUISEX.html

W. V. Quine was Edgar Pierce Professor of Philosophy, Harvard University . He wrote twenty-one books, thirteen of them published by Harvard University Press. Set Theory and Its Logic, Revised Edition W. V. Quine OTHER HARVARD BOOKS BY W. V. QUINE Elementary Logic, Revised Edition From a Logical Point of View: Nine Logico-Philosophical Essays, Second Revised Edition From Stimulus to Science Mathematical Logic, Revised Edition ... Theories and Things Belknap Press 380 pages Paperback edition ISBN 0-674-80207-1 Philosophy: General / Religion: General

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