Induction Bounding Weak Combinatorial Principles And The Homogeneous Model Theorem

Author : Denis Roman Hirschfeldt,Karen Lange,Richard A. Shore
Publisher : Unknown
Page : 101 pages
File Size : 40,9 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1470441411

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Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem by Denis Roman Hirschfeldt,Karen Lange,Richard A. Shore Pdf

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors sh.

Author : Denis R. Hirschfeldt,Karen Lange,Richard A. Shore
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 50,6 Mb
Release : 2017-09-25
Category : Computable functions
ISBN : 9781470426576

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Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem by Denis R. Hirschfeldt,Karen Lange,Richard A. Shore Pdf

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.

Author : Denis R Hirschfeldt
Publisher : World Scientific
Page : 232 pages
File Size : 45,9 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9789814612630

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Slicing the Truth by Denis R Hirschfeldt Pdf

This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions. Contents:Setting Off: An IntroductionGathering Our Tools: Basic Concepts and NotationFinding Our Path: König's Lemma and ComputabilityGauging Our Strength: Reverse MathematicsIn Defense of DisarrayAchieving Consensus: Ramsey's TheoremPreserving Our Power: ConservativityDrawing a Map: Five DiagramsExploring Our Surroundings: The World Below RT22Charging Ahead: Further TopicsLagniappe: A Proof of Liu's Theorem Readership: Graduates and researchers in mathematical logic. Key Features:This book assumes minimal background in mathematical logic and takes the reader all the way to current research in a highly active areaIt is the first detailed introduction to this particular approach to this area of researchThe combination of fully worked out arguments and exercises make this book well suited to self-study by graduate students and other researchers unfamiliar with the areaKeywords:Reverse Mathematics;Computability Theory;Computable Mathematics;Computable Combinatorics

Author : Damir D. Dzhafarov,Carl Mummert
Publisher : Springer Nature
Page : 498 pages
File Size : 46,6 Mb
Release : 2022-07-25
Category : Computers
ISBN : 9783031113673

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Reverse Mathematics by Damir D. Dzhafarov,Carl Mummert Pdf

Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.

Author : Nicola Gigli
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 42,9 Mb
Release : 2018-02-23
Category : Geometry, Differential
ISBN : 9781470427658

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Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below by Nicola Gigli Pdf

The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.

Author : Chin-Yu Hsiao
Publisher : American Mathematical Soc.
Page : 140 pages
File Size : 42,7 Mb
Release : 2018-08-09
Category : Electronic
ISBN : 9781470441012

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Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds by Chin-Yu Hsiao Pdf

Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.

Author : Alastair J. Litterick
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 55,8 Mb
Release : 2018-05-29
Category : Affine algebraic groups
ISBN : 9781470428372

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On Non-Generic Finite Subgroups of Exceptional Algebraic Groups by Alastair J. Litterick Pdf

Author : Roelof Bruggeman,Youngju Choie,Nikolaos Diamantis
Publisher : American Mathematical Soc.
Page : 167 pages
File Size : 49,8 Mb
Release : 2018-05-29
Category : Algebraic topology
ISBN : 9781470428556

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Holomorphic Automorphic Forms and Cohomology by Roelof Bruggeman,Youngju Choie,Nikolaos Diamantis Pdf

Author : Shouhei Honda
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 50,5 Mb
Release : 2018-05-29
Category : Geometry, Differential
ISBN : 9781470428549

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Elliptic PDEs on Compact Ricci Limit Spaces and Applications by Shouhei Honda Pdf

In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.

Author : Anne-Laure Dalibard,Laure Saint-Raymond
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 42,6 Mb
Release : 2018-05-29
Category : Boundary layer
ISBN : 9781470428358

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Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem by Anne-Laure Dalibard,Laure Saint-Raymond Pdf

Author : Cristian Anghel,Iustin Coandă,Nicolae Manolache
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 50,9 Mb
Release : 2018-05-29
Category : Chern classes
ISBN : 9781470428389

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Globally Generated Vector Bundles with Small C1 on Projective Spaces by Cristian Anghel,Iustin Coandă,Nicolae Manolache Pdf

Author : Sebastiano Carpi,Yasuyuki Kawahigashi,Roberto Longo,Mihály Weiner
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 43,8 Mb
Release : 2018-08-09
Category : Conformal invariants
ISBN : 9781470428587

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From Vertex Operator Algebras to Conformal Nets and Back by Sebastiano Carpi,Yasuyuki Kawahigashi,Roberto Longo,Mihály Weiner Pdf

The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.

Author : Zhou Gang,Dan Knopf,Israel Michael Siga
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 53,6 Mb
Release : 2018-05-29
Category : Asymptotic expansions
ISBN : 9781470428402

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Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow by Zhou Gang,Dan Knopf,Israel Michael Siga Pdf

Author : Matthew Harrison-Trainor
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 47,5 Mb
Release : 2018-05-29
Category : Angles (Geometry)
ISBN : 9781470428396

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Degree Spectra of Relations on a Cone by Matthew Harrison-Trainor Pdf

Author : John McCuan
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 49,5 Mb
Release : 2018-01-16
Category : Abelian groups
ISBN : 9781470409388

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The Stability of Cylindrical Pendant Drops by John McCuan Pdf

The author considers the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. He also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.