21. PhilSci Archive - Topos Theory As A Framework For Partial Truth topos theory as a Framework for Partial Truth. Butterfield, Jeremy(2000) topos theory as a Framework for Partial Truth. Full text http://philsci-archive.pitt.edu/archive/00000192/

About Browse Search Register ... Help Topos Theory as a Framework for Partial Truth Butterfield, Jeremy (2000) Topos Theory as a Framework for Partial Truth. Full text available as: PDF - Requires a viewer, such as Adobe Acrobat Reader or other PDF viewer. Postscript - Requires a viewer, such as GhostView - GSView Abstract This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical-such a valuation illuminates the Kochen-Specker theorem; in part mathematical-the valuations arise naturally in the theory of presheaves; and in part conceptual-the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2

22. Categories: Topos Theory And Large Cardinals categories topos theory and large cardinals. Andrej Bauer asked whether large cardinalsother than inaccessible ones have a natural definition in topos theory. http://north.ecc.edu/alsani/ct99-00(8-12)/msg00128.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Topos theory and large cardinals To categories@mta.ca Subject : categories: Topos theory and large cardinals From wlawvere@acsu.buffalo.edu Date : Tue, 21 Mar 2000 16:32:09 -0500 (EST) Reply-To wlawvere@acsu.buffalo.edu Sender cat-dist@mta.ca http://www.acsu.buffalo.edu/~wlawvere Prev by Date: categories: Preprint: a paper on injective hulls Next by Date: categories: Functorial injective hulls Prev by thread: categories: Topos theory and large cardinals Next by thread: categories: dom fibration Index(es): Date Thread

23. Categories: Topos Theory And Large Cardinals categories topos theory and large cardinals. To categories@mta.ca; Subjectcategories topos theory and large cardinals; From Andrej.Bauer@cs.cmu.edu; http://north.ecc.edu/alsani/ct99-00(8-12)/msg00117.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Topos theory and large cardinals To categories@mta.ca Subject : categories: Topos theory and large cardinals From Andrej.Bauer@cs.cmu.edu Date : 01 Mar 2000 22:29:58 -0500 Sender cat-dist@mta.ca Source-Info : Sender is really andrej+@gs2.sp.cs.cmu.edu User-Agent : Gnus/5.0803 (Gnus v5.8.3) XEmacs/20.4 (Emerald) Can you complete this analogy? ``Large cardinals are to ZFC, as are to topos theory.'' One answer is "Grothendieck universes", but they correspond to rather small large cardinals. Can we go further than that? Andrej Bauer School of Computer Science Carnegie Mellon University http://andrej.com Prev by Date: categories: Johnstone review of Clark/Davey Next by Date: categories: dom fibration Prev by thread: categories: Johnstone review of Clark/Davey Next by thread: categories: Topos theory and large cardinals Index(es): Date Thread

24. Course In Topos Theory topos theory, spring term 1999. synthetic differential geometry. This graduatecourse offers an introduction to topos theory and categorical logic. http://www.math.uu.se/~palmgren/topos-eng.html

Topos Theory, spring term 1999 A graduate course (6 course points) in mathematical logic. Topos theory grew out of the observation that the category of sheaves over a fixed topological space forms a universe of "continuously variable sets" which obeys the laws of intuitionistic logic. These sheaf models, or Grothendieck toposes, turn out to be generalisations of Kripke and Beth models (which are fundamental for various non-classical logics) as well as Cohen's forcing models for set theory. The notion of topos was subsequently extended and given an elementary axiomatisation by Lawvere and Tierney, and shown to correspond to a certain higher order intuitionistic logic. Various logics and type theories have been given categorical characterisations, which are of importance for the mathematical foundations for programming languages. One of the most interesting aspects of toposes is that they can provide natural models of certain theories that lack classical models, viz. synthetic differential geometry. This graduate course offers an introduction to topos theory and categorical logic. In particular the following topics will be covered: Categorical logic: relation between logics, type theories and categories. Generalised topologies, including formal topologies. Sheaves. Pretoposes and toposes. Beth-Kripke-Joyal semantics. Boolean toposes and Cohen forcing. Barr's theorem and Diaconescu covers. Geometric morphisms. Classifying toposes. Sheaf models of infinitesimal analysis.

25. Kurs I Toposteori Springer 1992. Referenslitteratur PT Johnstone. topos theory. Academic Press 1977.J. Lambek and PJ Scott An introduction to Higher Order Categorical Logic. http://www.math.uu.se/~palmgren/topos.html

Toposteori, vt-99 En forskarutbildningskurs (6p) i matematisk logik. (In English, Please.) Schema: Kurslitteratur: S. Mac Lane and I. Moerdijk: Sheaves in Geometry and Logic. Springer 1992. Referenslitteratur: P.T. Johnstone. Topos Theory. Academic Press 1977. J. Lambek and P.J. Scott: An introduction to Higher Order Categorical Logic. Cambridge University Press 1986 S. Mac Lane: Categories for the Working Mathematician. Springer 1971. A.M. Pitts. Categorical Logic. Chapter in the Handbook of Logic in Computer Science, vol. VI. Oxford University Press (under utgivning) Aktuell kursinformation : hittills behandlade moment etc. 1999-02-15, Erik Palmgren

26. [math/0207028] Homotopical Algebraic Geometry I: Topos Theory Oct 2002 114917 GMT (88kb) Homotopical Algebraic Geometry I Topostheory. Authors Bertrand Toen, Gabriele Vezzosi Comments 104 http://arxiv.org/abs/math/0207028

Mathematics, abstract math.AG/0207028 From: Gabriele Vezzosi [ view email ] Date ( ): Tue, 2 Jul 2002 20:44:00 GMT (86kb) Date (revised ): Tue, 8 Oct 2002 11:49:17 GMT (88kb) Date (revised v3): Tue, 10 Feb 2004 17:04:03 GMT (84kb) Homotopical Algebraic Geometry I: Topos theory Authors: Bertrand Toen Gabriele Vezzosi Comments: 71 pages. Some expositional changes suggested by the referee, and a new section with the proof of Giraud Theorem for model topoi Subj-class: Algebraic Geometry; Algebraic Topology MSC-class: Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

27. [gr-qc/9910005] Some Possible Roles For Topos Theory In Quantum Theory And Quant From Chris Isham view email Date Sat, 2 Oct 1999 133957 GMT (28kb) SomePossible Roles for topos theory in Quantum Theory and Quantum Gravity. http://arxiv.org/abs/gr-qc/9910005

General Relativity and Quantum Cosmology, abstract gr-qc/9910005 From: Chris Isham [ view email ] Date: Sat, 2 Oct 1999 13:39:57 GMT (28kb) Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity Authors: C.J. Isham J.Butterfield Comments: Report-no: Imperial/TP/98-99/76 Journal-ref: Found.Phys. 30 (2000) 1707-1735 We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4, we draw some conclusions. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

28. An Introduction To Fibrations, Topos Theory, The Effective Topos And Modest Sets An introduction to fibrations, topos theory, the effective topos and modestsets. Abstract A topos is a categorical model of constructive set theory. http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208/

An introduction to fibrations, topos theory, the effective topos and modest sets Wesley Phoa Abstract: A topos is a categorical model of constructive set theory. In particular, the effective topos is the categorical `universe' of recursive mathematics. Among its objects are the modest sets , which form a set-theoretic model for polymorphism. More precisely, there is a fibration of modest sets which satisfies suitable categorical completeness properties, that make it a model for various polymorphic type theories. These lecture notes provide a reasonably thorough introduction to this body of material, aimed at theoretical computer scientists rather than topos theorists. Chapter 2 is an outline of the theory of fibrations, and sketches how they can be used to model various typed lambda-calculi. Chapter 3 is an exposition of some basic topos theory, and explains why a topos can be regarded as a model of set theory. Chapter 4 discusses the classical PER model for polymorphism, and shows how it `lives inside' a particular topos - the effective topos - as the category of modest sets. An appendix contains a full presentation of the internal language of a topos, and a map of the effective topos. Chapters 2 and 3 provide a sampler of categorical type theory and categorical logic, and should be of more general interest than Chapter 4. They can be read more or less independently of each other; a connection is made at the end of Chapter 3.

29. Homotopical Algebraic Geometry I Topos Theory, By Bertrand Toen And Gabriele Vez Homotopical Algebraic Geometry I topos theory, by Bertrand Toen andGabriele Vezzosi. This is the first of a series of papers devoted http://www.math.uiuc.edu/K-theory/0579/

Homotopical Algebraic Geometry I Topos theory, by Bertrand Toen and Gabriele Vezzosi 0579.bib (254 bytes) agmod-I-fin-web.dvi (516636 bytes) [July 2, 2002] agmod-I-fin-web.dvi.gz (185402 bytes) agmod-I-fin-web.ps.gz (345410 bytes) Bertrand Toen Gabriele Vezzosi

30. Re: Topos Theory For Physicists Re topos theory for physicists. Subject Re topos theory for physicists;From baez@galaxy.ucr.edu (John Baez); Date Mon, 1 Jan 2001 054218 GMT; http://www.lns.cornell.edu/spr/2001-01/msg0030351.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re: Topos theory for physicists Subject : Re: Topos theory for physicists From : baez@galaxy.ucr.edu (John Baez) Date : Mon, 1 Jan 2001 05:42:18 GMT Approved : mmcirvin@world.std.com (sci.physics.research) Newsgroups : sci.physics.research Organization : UCR References Sender : mmcirvin@world.std.com (Matthew J McIrvin) Prev by Date: Re: A Philosophical Query and Comment about Quantizing Gravity Next by Date: Re: Hopf algebras, quantum groups Prev by thread: Re: A Philosophical Query and Comment about Quantizing Gravity Next by thread: Re: Topos theory for physicists Index(es): Date Thread

31. Re: Topos Theory For Physicists Index Re topos theory for physicists. Subject Re topos theoryfor physicists; From Chris Hillman hillman@math.washington.edu ; http://www.lns.cornell.edu/spr/2001-01/msg0030379.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re: Topos theory for physicists Subject : Re: Topos theory for physicists From Date : Thu, 4 Jan 2001 02:44:17 GMT Approved : mmcirvin@world.std.com (sci.physics.research) In-Reply-To Newsgroups : sci.physics.research Organization : University of Washington References Sender : mmcirvin@world.std.com (Matthew J McIrvin) http://www.math.washington.edu/~hillman/papers.html http://www.math.washington.edu/~hillman/ Prev by Date: Re: Scale invariant general relativity? Next by Date: Re: Self-learning quantum mechanics Prev by thread: Re: Topos theory for physicists Next by thread: Re: Hopf algebras, quantum groups Index(es): Date Thread

32. On Branched Covers In Topos Theory On Branched Covers in topos theory. Jonathon Funk. We present somenew findings concerning branched covers in topos theory. Our http://www.tac.mta.ca/tac/volumes/7/n1/7-01abs.html

On Branched Covers in Topos Theory Jonathon Funk We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox, of the including topos. We also have some new results concerning the general theory of KZ-doctrines, such as the closure under composition of discrete fibrations for a KZ-doctrine, in the sense of Bunge and Funk. Keywords: 1991 MSC: 18B25. Theory and Applications of Categories , Vol. 7, 2000, No. 1, pp 1-22. http://www.tac.mta.ca/tac/volumes/7/n1/n1.dvi http://www.tac.mta.ca/tac/volumes/7/n1/n1.ps http://www.tac.mta.ca/tac/volumes/7/n1/n1.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n1/n1.dvi ... TAC Home

33. Categorical Logic Using sheaves, topos theory also subsumes Kripke semantics for intuitionisticlogic. Prerequisites. 80413/713 Category Theory, or equivalent. http://www.andrew.cmu.edu/user/awodey/catlog/

Categorical Logic Fall 2002 Course Information Instructor: Steve Awodey Office: Baker 152 (mail: Baker 135) Office Hour: Thursday 1-2, or by appointment Phone: 8947 Email: awodey@andrew Secretary: Baker 135 Overview This course focuses on applications of category theory in logic and computer science. A leading idea is functorial semantics, according to which a model of a logical theory is a set-valued functor on a structured category determined by the theory. This gives rise to a syntax-invariant notion of a theory and introduces many algebraic methods into logic, leading naturally to the universal and other general models that distinguish functorial from classical semantics. Such categorical models occur, for example, in denotational semantics. In this connection the lambda-calculus is treated via the theory of cartesian closed categories. Similarly higher-order logic is modelled by the categorical notion of a topos. Using sheaves, topos theory also subsumes Kripke semantics for intuitionistic logic. Prerequisites 80-413/713 Category Theory, or equivalent.

34. OUP: Sketches Of An Elephant: A Topos Theory Compendium: Johnstone Sketches of an Elephant A topos theory Compendium 2 Volume Set. PeterT. Johnstone, Reader in the Foundations of Mathematics, University http://www.oup.co.uk/isbn/0-19-852496-X

VIEW BASKET Quick Links About OUP Career Opportunities Contacts Need help? oup.com Search the Catalogue Site Index American National Biography Booksellers' Information Service Children's Fiction and Poetry Children's Reference Dictionaries Dictionary of National Biography Digital Reference English Language Teaching Higher Education Textbooks Humanities International Education Unit Journals Law Medicine Music Oxford English Dictionary Reference Rights and Permissions Science School Books Social Sciences World's Classics UK and Europe Book Catalogue Help with online ordering How to order Postage Returns policy ... Table of contents Sketches of an Elephant: A Topos Theory Compendium - 2 Volume Set Peter T. Johnstone , Reader in the Foundations of Mathematics, University of Cambridge, Cambridge, UK 0-19-852496-X Publication date: 12 September 2002 Clarendon Press 1600 pages, -, 234mm x 156mm Series: Oxford Logic Guides Search for titles in the same series Ordering Individual customers order by phone, post, or fax Teachers in UK and European schools (and FE colleges in the UK): order by phone, post, or fax

35. A Link On Topos Theory (not Too Hard) A link on topos theory (not too hard). In Reply to Re Natures New Math(topos theory?) posted by DickT on July 19, 2002 at 111618 sol,. http://superstringtheory.com/forum/philboard/messages13/202.html

String Theory Discussion Forum String Theory Home Forum Index A link on Topos theory (not too hard) Follow Ups Post Followup Philosophy of Physics XIII FAQ Posted by DickT on July 19, 2002 at 19:34:32: In Reply to: Re: Natures New Math( Topos Theory?) posted by DickT on July 19, 2002 at 11:16:18: sol, I found this Topos Paper . Chris Isham is a coauthor, he is a big name in this area. The first three sections are very clear (to me) and maybe give you an idea. I know you understand better from pictures, but there don't seem to be any. Regards, Dick (Report this post to the moderator) Follow Ups: (Reload page to see most recent) Re: A link on Topos theory (not too hard) sol Post a Followup Follow Ups Post Followup Philosophy of Physics XIII FAQ

36. Re: Natures New Math( Topos Theory?) Re Natures New Math( topos theory?). In Reply to Natures New Math( topos theory?)posted by sol on July 18, 2002 at 150855 Sol,. Always welcome. http://superstringtheory.com/forum/philboard/messages13/195.html

String Theory Discussion Forum String Theory Home Forum Index Re: Natures New Math( Topos Theory?) Follow Ups Post Followup Philosophy of Physics XIII FAQ Posted by DickT on July 18, 2002 at 20:02:51: In Reply to: Natures New Math( Topos Theory?) posted by sol on July 18, 2002 at 15:08:55: Sol, Always welcome. I have stayed away from topos thory because it requires a thorough grounding in category theory, and that's likely to be a long slog. CT is something it's easy to get the basics of, but very hard to get the depth of - sort of like Go. Regard, Dick (Report this post to the moderator) Follow Ups: (Reload page to see most recent) Re: Natures New Math( Topos Theory?) sol Re: Natures New Math( Topos Theory?) DickT ... sol Post a Followup Follow Ups Post Followup Philosophy of Physics XIII FAQ

37. October2 topos theory in Logic and Computer Science I. Professor Noson S. YanofskyBrooklyn College of CUNY noson@sci.brooklyn.cuny.edu. Login. http://nylogic.org/Workshop/Fall1998/October2

nylogic.org Workshop Calendar This Week ... Friday, October 2, 1998 2:00 pm Room 512 120 minutes Topos Theory in Logic and Computer Science I Professor Noson S. Yanofsky Brooklyn College of CUNY noson@sci.brooklyn.cuny.edu ... Login

38. Sketches Of An Elephant: A Topos Theory Compendium: 2 Volume Set (Oxford Logic G Sketches of an Elephant a topos theory Compendium 2 Volume Set(Oxford Logic Guides) Peter T Johnstone. Sketches of an Elephant http://www.welsh-breaks.co.uk/Peter-T-Johnstone-Sketches-of-an-Elephant-920-803-

Sketches of an Elephant: a Topos Theory Compendium: 2 Volume Set (Oxford Logic Guides) Peter T Johnstone Author or Artist : Peter T Johnstone Title: Sketches of an Elephant: a Topos Theory Compendium: 2 Volume Set (Oxford Logic Guides) Johnstone Peter T Peter T. Johnstone Subject: Geometry Category: Computers Internet Computer Science Information Systems General Format: Hardcover Ramdas Ram-Mohan-Finite Element and Boundary Element Applications in Quantum Mechanics (Oxford Applied and Engineering Mathematics)... Simon Goldhill-The Invention of Prose (New Surveys in the Classics)... Russell Lande Steinar Engen Bernt-Erik Saether-Stochastic Population Dynamics in Ecology and Conservation (Oxford Series in Ecology and Evolution)... Normal and Defective Colour Vision... ... Doris Lessing-The Sentimental Agents in the Volyen Empire...

39. Fiche Document -Topos Theory Translate this page Ouvrage - Cote 00000014 - (disponible) topos theory Johnstone, PT (Principal)London NY San Francisco Academic Press 1977 catégorie cohomologie http://bibli.cirm.univ-mrs.fr/Document.htm&numrec=031027335920910

40. Homepage Of Jeremy Butterfield In recent years, I have mostly worked on philosophical aspects of quantum gravityand on applying topos theory to quantum theory (especially the KochenSpecker http://users.ox.ac.uk/~alls0074/

Homepage of Jeremy Butterfield I am a Senior Research Fellow at All Souls College, University of Oxford, and a member of the Philosophy Faculty. My main research interests are philosophy of quantum theory and philosophy of relativity. In recent years, I have mostly worked on philosophical aspects of quantum gravity and on applying topos theory to quantum theory (especially the Kochen-Specker 'no go' theorem). But I expect in coming years to work mainly in the following two areas. (1): Philosophical aspects of quantum field theory. I am interested especially in the following topics: nonlocality, localization and the emergence of particles, renormalization, and the gauge structures of quantum field theories. (2): Philosophical aspects of quantum information. email: jb56@cus.cam.ac.uk Click on the following, to download as pdf or ps files. Some Recent and Forthcoming Papers 'Quantum Curiosities of Psychophysics' , in Consciousness and Human Identity , ed. J. Cornwell, Oxford University Press, 1998; 122-157. Also at: PITT-PHIL-SCI00000193 'The State of Physics: Halfway through the Woods' The Journal of Soft Computing 'Topos Theory as a Framework for Partial Truth' , forthcoming in P. Gardenfors, K. Kijania-Placek and J. Wolenski (ed.)

Page 2     21-40 of 95    Back | 1  | 2  | 3  | 4  | 5  | Next 20