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Author : Andreas Blass,Andrej Ščedrov
Publisher : Unknown
Page : 134 pages
File Size : 42,6 Mb
Release : 1989
Category : Axiom of choice
ISBN : 1470408244
Author : Andreas Blass,Andrej Ščedrov
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 46,5 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821824689
Author : S. Barry Cooper
Publisher : Cambridge University Press
Page : 384 pages
File Size : 47,6 Mb
Release : 2009
Category : Logic, Symbolic and mathematical
ISBN : 9780521110815
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
Author : Yiannis N. Moschovakis
Publisher : Springer Science & Business Media
Page : 607 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461228226
The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences. We meant to have a conference which would bring together the LICS commu nity with some of the more traditional "mathematical logicians" and where the emphasis would be on the flow of ideas from computer science to logic rather than the other way around. In a LICS talk, sometimes, the speaker presents a perfectly good theorem about (say) the A-calculus or finite model theory in terms of its potential applications rather than its (often more ob vious) intrinsic, foundational interest and intricate proof. This is not meant to be a criticism; the LICS meetings are, after all, organized by the IEEE Computer Society. We thought, for once, it would be fun to see what we would get if we asked the speakers to emphasize the relevance of their work for logic rather than computer science and to point out what is involved in the proofs. I think, mostly, it worked. In any case, the group of people represented as broad a selection of logicians as I have seen in recent years, and the quality of the talks was (in my view) exceptionally, unusually high. I learned a lot and (I think) others did too.
Author : American Mathematical Society. Meeting
Publisher : American Mathematical Soc.
Page : 307 pages
File Size : 40,5 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821850329
Mathematicians interested in understanding the directions of current research in set theory will not want to overlook this book, which contains the proceedings of the AMS Summer Research Conference on Axiomatic Set Theory, held in Boulder, Colorado, June 19-25, 1983. This was the first large meeting devoted exclusively to set theory since the legendary 1967 UCLA meeting, and a large majority of the most active research mathematicians in the field participated. All areas of set theory, including constructibility, forcing, combinatorics and descriptive set theory, were represented; many of the papers in the proceedings explore connections between areas. Readers should have a background of graduate-level set theory. There is a paper by S. Shelah applying proper forcing to obtain consistency results on combinatorial cardinal 'invariants' below the continuum, and papers by R. David and S. Freidman on properties of $0^\ No. $.Papers by A. Blass, H.D. Donder, T. Jech and W. Mitchell involve inner models with measurable cardinals and various combinatorial properties. T. Carlson largely solves the pin-up problem, and D. Velleman presents a novel construction of a Souslin tree from a morass. S. Todorcevic obtains the strong failure of the \qedprinciple from the Proper Forcing Axiom and A. Miller discusses properties of a new species of perfect-set forcing. H. Becker and A. Kechris attack the third Victoria Delfino problem while W. Zwicker looks at combinatorics on $P_\kappa(\lambda)$ and J. Henle studies infinite-exponent partition relations. A. Blass shows that if every vector space has a basis then $AC$ holds. I. Anellis treats the history of set theory, and W. Fleissner presents set-theoretical axioms of use in general topology.
Author : D.M. Gabbay,Franz Guenthner
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 44,9 Mb
Release : 2005-12-15
Category : Philosophy
ISBN : 9781402030925
The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications
Author : Steven Zelditch
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 52,8 Mb
Release : 1992
Category : Curves on surfaces
ISBN : 9780821825266
This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.
Author : Robert Goldblatt
Publisher : Courier Corporation
Page : 578 pages
File Size : 41,6 Mb
Release : 2013-07-25
Category : Mathematics
ISBN : 9780486317960
A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.
Author : P. T. Johnstone
Publisher : Oxford University Press
Page : 836 pages
File Size : 51,8 Mb
Release : 2002-09-12
Category : Computers
ISBN : 0198515987
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
Author : Anonim
Publisher : Elsevier
Page : 878 pages
File Size : 42,8 Mb
Release : 2012-01-24
Category : Mathematics
ISBN : 9780080930664
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Author : Bruce Arie Reznick
Publisher : American Mathematical Soc.
Page : 155 pages
File Size : 55,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825235
This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.
Author : John D. Fay
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 54,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825501
This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.
Author : Shari A. Prevost
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 42,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825273
We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.
Author : A.k. Sharma
Publisher : Discovery Publishing House
Page : 290 pages
File Size : 48,9 Mb
Release : 2009
Category : Algebra
ISBN : 8183564526
Author : Saunders MacLane,Ieke Moerdijk
Publisher : Springer Science & Business Media
Page : 643 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209270
Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.