Semigroups Underlying First Order Logic PDF Download
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| Author | : William Craig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 298 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821841491 |
Download Semigroups Underlying First-Order Logic Book in PDF, ePub and Kindle
Boolean, relation-induced, and other operations for dealing with first-order definability Uniform relations between sequences Diagonal relations Uniform diagonal relations and some kinds of bisections or bisectable relations Presentation of ${\mathbf S}_q$, ${\mathbf S}_p$ and related structures Presentation of ${\mathbf S}_{pq}$, ${\mathbf S}_{pe}$ and related structures Appendix. Presentation of ${\mathbf S}_{pqe}$ and related structures Bibliography Index of symbols Index of phrases and subjects List of relations involved in presentations Synopsis of presentations
| Author | : Hajnal Andréka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 457 |
| Release | : 2014-01-27 |
| Genre | : Mathematics |
| ISBN | : 3642350259 |
Download Cylindric-like Algebras and Algebraic Logic Book in PDF, ePub and Kindle
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
| Author | : Dominic Verity |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 208 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821841424 |
Download Complicial Sets Characterising the Simplicial Nerves of Strict $\omega $-Categories Book in PDF, ePub and Kindle
The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.
| Author | : Sonia Natale |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 138 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821839489 |
Download Semisolvability of Semisimple Hopf Algebras of Low Dimension Book in PDF, ePub and Kindle
The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
| Author | : Robert M. Guralnick |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 142 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821839926 |
Download Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points Book in PDF, ePub and Kindle
Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.
| Author | : Gail Letzter |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 104 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821841319 |
Download Invariant Differential Operators for Quantum Symmetric Spaces Book in PDF, ePub and Kindle
This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
| Author | : Yoshikata Kida |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 206 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821841963 |
Download The Mapping Class Group from the Viewpoint of Measure Equivalence Theory Book in PDF, ePub and Kindle
The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent. Moreover, the author gives various examples of discrete groups which are not measure equivalent to the mapping class groups. In the course of the proof, the author investigates amenability in a measurable sense for the actions of the mapping class group on the boundary at infinity of the curve complex and on the Thurston boundary and, using this investigation, proves that the mapping class group of a compact orientable surface is exact.
| Author | : Gelu Popescu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821839128 |
Download Entropy and Multivariable Interpolation Book in PDF, ePub and Kindle
We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive multi-Toeplitz kernels on free semigroups (resp. multi-analytic operators) and consequences concerning the extreme points of the unit ball of the noncommutative analytic Toeplitz algebra $F ninfty$. We obtain several geometric characterizations of the central intertwining lifting, a maximal principle, and a permanence principle for the noncommutative commutant lifting theorem. Under certain natural conditions, we find explicit forms for the maximal entropy solution of this multivariable commutant lifting theorem. All these results are used to solve maximal entropy interpolation problems in several variables. We obtain explicit forms for the maximal entropy solution (as well as its entropy) of the Sarason, Caratheodory-Schur, and Nevanlinna-Pick type interpolation problems for the noncommutative (resp. commutative) analytic Toeplitz algebra $F ninfty$ (resp. $W ninfty$) and their tensor products with $B({\mathcal H , {\mathcal K )$. In particular, we provide explicit forms for the maximal entropy solutions of several interpolation problems on the unit ball of $\mathbb{C n$.
| Author | : Ron Donagi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 104 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821840924 |
Download Torus Fibrations, Gerbes, and Duality Book in PDF, ePub and Kindle
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form
| Author | : Salah-Eldin Mohammed |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 120 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821842501 |
Download The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations Book in PDF, ePub and Kindle
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
