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Walks On Ordinals And Their Characteristics
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Book Synopsis Walks on Ordinals and Their Characteristics by : Stevo Todorcevic
Download or read book Walks on Ordinals and Their Characteristics written by Stevo Todorcevic and published by Springer Science & Business Media. This book was released on 2007-12-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The walks on ordinals and analysis of their characteristics is a subject matter started by the author some twenty years ago in order to disprove a particular extension of the Ramsey theorem. A further analysis has shown however that the resulting method is quite useful in detecting critical mathematical objects in contexts where only rough classifications are possible. The book gives a careful and comprehensive account of the method and gathers many of these applications in a unified and comprehensive manner.
Book Synopsis Handbook of Set Theory by : Matthew Foreman
Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Book Synopsis Sets and Extensions in the Twentieth Century by :
Download or read book Sets and Extensions in the Twentieth Century written by and published by Elsevier. This book was released on 2012-01-24 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Foundations of Mathematics by : Andrés Eduardo Caicedo
Download or read book Foundations of Mathematics written by Andrés Eduardo Caicedo and published by American Mathematical Soc.. This book was released on 2017-05-12 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
Author : Publisher :World Scientific ISBN 13 : Total Pages :1191 pages Book Rating :4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1191 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by : Rajendra Bhatia
Download or read book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Book Synopsis Walks on Ordinals and Their Characteristics by : Stevo Todorc̆ević
Download or read book Walks on Ordinals and Their Characteristics written by Stevo Todorc̆ević and published by . This book was released on 2007 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Set Theory by : Paul B. Larson
Download or read book Geometric Set Theory written by Paul B. Larson and published by American Mathematical Soc.. This book was released on 2020-07-16 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Book Synopsis Logic Colloquium 2006 by : S. Barry Cooper
Download or read book Logic Colloquium 2006 written by S. Barry Cooper and published by Cambridge University Press. This book was released on 2009 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Notes On Forcing Axioms by : Stevo Todorcevic
Download or read book Notes On Forcing Axioms written by Stevo Todorcevic and published by World Scientific. This book was released on 2013-12-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach-Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.
Book Synopsis Stable Homotopy Around the Arf-Kervaire Invariant by : Victor P. Snaith
Download or read book Stable Homotopy Around the Arf-Kervaire Invariant written by Victor P. Snaith and published by Springer Science & Business Media. This book was released on 2009-03-28 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .
Book Synopsis Recent Progress in General Topology III by : K.P. Hart
Download or read book Recent Progress in General Topology III written by K.P. Hart and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Book Synopsis Extended Abstracts EuroComb 2021 by : Jaroslav Nešetřil
Download or read book Extended Abstracts EuroComb 2021 written by Jaroslav Nešetřil and published by Springer Nature. This book was released on 2021-08-23 with total page 875 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.
Download or read book Fundamenta Mathematicae written by and published by . This book was released on 2013 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Israel Journal of Mathematics by : Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel)
Download or read book Israel Journal of Mathematics written by Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel) and published by . This book was released on 2008 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis and Discrete Potential Theory by : M.A. Picardello
Download or read book Harmonic Analysis and Discrete Potential Theory written by M.A. Picardello and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S.S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J
Book Synopsis Graphs and Networks by : Armen H. Zemanian
Download or read book Graphs and Networks written by Armen H. Zemanian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book examines results on transfinite graphs and networks achieved through continued research effort over the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Permissive Electrical Networks. Specific topics covered include connectedness ideas, distance ideas, and nontransitivity of connectedness. The book will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.
