Results 1 - 10 of 13

Finitary Galois Extensions over non-commutative bases

by Imre Bálint, Kornél Szlachányi , 2005
"... We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various cla ..."
Abstract - Cited by 13 (2 self) - Add to MetaCart
commutative algebras play the role of noncommutative scalar extensions by a slightly generalized Brzeziński-Militaru Theorem. Contravariant ”fiber functors ” are used to prove an analogue of Ulbrich’s Theorem and to get a monoidal embedding of the module category ME of the endomorphism Hopf algebroid E = End

Norm convergence of multiple ergodic averages for commuting transformations

by Terence Tao , 2007
"... Let T1,..., Tl: X → X be commuting measure-preserving transformations on a probability space (X, X, µ). We show that the multiple ergodic averages 1 PN−1 N n=0 f1(T n 1 x)... fl(T n l x) are convergent in L2 (X, X, µ) as N → ∞ for all f1,..., fl ∈ L ∞ (X, X, µ); this was previously established fo ..."
Abstract - Cited by 81 (4 self) - Add to MetaCart
developments regarding the hypergraph regularity and removal lemmas, although we will not need the full strength of those lemmas. In particular, the l = 2 case of our arguments are a finitary analogue of those in [2].

FOR RANDOM ACCESS MACHINES

by Iwolfgang Maasst , 1985
"... Abstr¡ct. wc prove optimal lower bounds on the computation time for several well-known test problems on u quiå realistic computational model: the random access machine ' These lower bound arguments may be of special intefest for logicians because they rely on finitary analogues of two importai ..."
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Abstr¡ct. wc prove optimal lower bounds on the computation time for several well-known test problems on u quiå realistic computational model: the random access machine ' These lower bound arguments may be of special intefest for logicians because they rely on finitary analogues of two importai

On Digraph Coloring Problems and Treewidth Duality

by Albert Atserias - 20th IEEE Symposium on Logic in Computer Science (LICS , 2005
"... It is known that every constraint-satisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifierfree. Using this, we illustrate the power of the logical approach to CSPs ..."
Abstract - Cited by 53 (2 self) - Add to MetaCart
by resolving two conjectures about treewidth duality in the digraph case. The point is that the analogues of these conjectures for general CSPs were resolved long ago by proof techniques that break down for digraphs. We also completely characterize those CSPs that are first-order definable and show

Weight and measure in NIP theories

by Anand Pillay , 2011
"... We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue (for NIP theories) of the fact that a stable theory T is “strongly dependent ” if and only if all (finitary) types have finite weight. 1 ..."
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We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue (for NIP theories) of the fact that a stable theory T is “strongly dependent ” if and only if all (finitary) types have finite weight. 1

Wadge Hierarchy of Omega Context Free Languages

by Olivier Finkel - THEORETICAL COMPUTER SCIENCE , 2001
"... We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In: ”A Decade of Concurrency”, Springer LNCS 803 (1994), 583-621], proving topological properties of omega context free languages (ω-CFL) which extend those of [O. Finkel, Top ..."
Abstract - Cited by 23 (21 self) - Add to MetaCart
in the Proceedings of the 1990 Workshop ”Logics and Recognizable Sets”] and of Simonnet [Automates et Théorie Descriptive, Ph.D. Thesis, Universite ́ Paris 7, March 1992] about ω-powers of finitary languages, giving an example of a finitary context free language L such that Lω is not a Borel set. Then we prove some

Saturated models of universal theories

by Jeremy Avigad , 2001
"... A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yield-ing uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet ..."
Abstract - Cited by 9 (5 self) - Add to MetaCart
A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yield-ing uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet

Towards a Theory of Recursive Structures

by David Harel - In Proceedings of 23rd International Symposium on Mathematical Foundations of Computer Science MFCS 98 , 1998
"... In computer science, one is interested mainly in finite objects. Insofar as infinite objects are of interest, they must be computable, i.e., recursive, thus admitting an effective finite representation. This leads to the notion of a recursive graph, or, more generally, a recursive structure, model o ..."
Abstract - Cited by 15 (1 self) - Add to MetaCart
or data base. This paper summarizes recent work on recursive structures and data bases, including (i) the high undecidability of many problems on recursive graphs and structures, (ii) a method for deducing results on the descriptive complexity of finitary NP optimization problems from results

Interpretations in trees with countably many branches

by Alexander Rabinovich, Sasha Rubin - In LICS , 2012
"... Abstract—We study the expressive power of logical interpreta-tions on the class of scattered trees, namely those with countably many infinite branches. Scattered trees can be thought of as the tree analogue of scattered linear orders. Every scattered tree has an ordinal rank that reflects the struct ..."
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Abstract—We study the expressive power of logical interpreta-tions on the class of scattered trees, namely those with countably many infinite branches. Scattered trees can be thought of as the tree analogue of scattered linear orders. Every scattered tree has an ordinal rank that reflects

AND SKOLEM FUNCTIONS

by Christopher S. Shaw, Doctor Of Philosophy, Weakly O-minimal Structures, Christopher S. Shaw, S. Shaw , 2008
"... The monotonicity theorem is the first step in proving that o-minimal structures satisfy cellular decomposition, which gives a comprehensive picture of the definable subsets in an o-minimal structure. This leads to the fact that any o-minimal struc-ture has an o-minimal theory. We first investigate t ..."
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the possible analogues for mono-tonicity in a weakly o-minimal structure, and find that having definable Skolem functions and uniform elimination of imaginaries is sufficient to guarantee that a weakly o-minimal theory satisfies one of these, the Finitary Monotonicity Property. In much of the work on weakly o
Results 1 - 10 of 13