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Author: Dominique Lecomte
Publisher: American Mathematical Soc.
ISBN: 0821875574
Category : Mathematics
Languages : en
Pages : 95
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Book Description
Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\!\leq\! d\!\leq\!\omega$ be a cardinal. A Borel subset $B$ of ${\mathbb R}^d$ is potentially in $\bf\Gamma$ if there is a finer Polish topology on $\mathbb R$ such that $B$ is in $\bf\Gamma$ when ${\mathbb R}^d$ is equipped with the new product topology. The author provides a way to recognize the sets potentially in $\bf\Gamma$ and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.
Author: Dominique Lecomte
Publisher: American Mathematical Soc.
ISBN: 0821875574
Category : Mathematics
Languages : en
Pages : 95
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Book Description
Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\!\leq\! d\!\leq\!\omega$ be a cardinal. A Borel subset $B$ of ${\mathbb R}^d$ is potentially in $\bf\Gamma$ if there is a finer Polish topology on $\mathbb R$ such that $B$ is in $\bf\Gamma$ when ${\mathbb R}^d$ is equipped with the new product topology. The author provides a way to recognize the sets potentially in $\bf\Gamma$ and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.
Author: Dag Prawitz
Publisher: Elsevier
ISBN: 0444893415
Category : Electronic books
Languages : en
Pages : 1006
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Book Description
This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.
Author: D. Prawitz
Publisher: Elsevier
ISBN: 0080544959
Category : Mathematics
Languages : en
Pages : 1005
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Book Description
This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.
Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 113950424X
Category : Mathematics
Languages : en
Pages : 549
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Book Description
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Author:
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 656
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Book Description
Author: Andrzej Nagórko
Publisher: American Mathematical Soc.
ISBN: 082185366X
Category : Mathematics
Languages : en
Pages : 106
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Book Description
The author develops a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nobeling manifold characterization conjecture.
Author: Thomas Lam
Publisher: American Mathematical Soc.
ISBN: 082187294X
Category : Mathematics
Languages : en
Pages : 113
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Book Description
The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.
Author: Joachim Krieger
Publisher: American Mathematical Soc.
ISBN: 082184489X
Category : Mathematics
Languages : en
Pages : 111
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Book Description
This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain ``microlocal geometric renormalization'' of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.
Author: Ariel Barton
Publisher: American Mathematical Soc.
ISBN: 0821887408
Category : Mathematics
Languages : en
Pages : 120
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Book Description
In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. He shows that for such operators, the Dirichlet problem with boundary data in $L^q$ can be solved for $q1$ small enough, and provide an endpoint result at $p=1$.
Author: David I. Stewart
Publisher: American Mathematical Soc.
ISBN: 0821883321
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Let $G=G(K)$ be a simple algebraic group defined over an algebraically closed field $K$ of characteristic $p\geq 0$. A subgroup $X$ of $G$ is said to be $G$-completely reducible if, whenever it is contained in a parabolic subgroup of $G$, it is contained in a Levi subgroup of that parabolic. A subgroup $X$ of $G$ is said to be $G$-irreducible if $X$ is in no proper parabolic subgroup of $G$; and $G$-reducible if it is in some proper parabolic of $G$. In this paper, the author considers the case that $G=F_4(K)$. The author finds all conjugacy classes of closed, connected, semisimple $G$-reducible subgroups $X$ of $G$. Thus he also finds all non-$G$-completely reducible closed, connected, semisimple subgroups of $G$. When $X$ is closed, connected and simple of rank at least two, he finds all conjugacy classes of $G$-irreducible subgroups $X$ of $G$. Together with the work of Amende classifying irreducible subgroups of type $A_1$ this gives a complete classification of the simple subgroups of $G$. The author also uses this classification to find all subgroups of $G=F_4$ which are generated by short root elements of $G$, by utilising and extending the results of Liebeck and Seitz.
