An algebraic and logical approach to continuous images
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Klaas Pieter Hart (2002)
Acta Universitatis Carolinae. Mathematica et Physica
Christian Delhommé (1999)
Fundamenta Mathematicae
A first order structure with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their...
Pomper, Markus (2004)
International Journal of Mathematics and Mathematical Sciences
Antoine Ducros (2013)
Confluentes Mathematici
R. Cluckers, L. Lipshitz (2011)
Journal of the European Mathematical Society
Rahim Moosa, Sergei Starchenko (2008)
Fundamenta Mathematicae
It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.
Dana Bartošová, Aleksandra Kwiatkowska (2015)
Fundamenta Mathematicae
We show that a natural quotient of the projective Fraïssé limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of the Lelek fan and of its homeomorphism group. We show that the Lelek fan is projectively universal and projectively ultrahomogeneous in the class of smooth fans. We further show that the homeomorphism group of the Lelek fan is totally disconnected, generated by every neighbourhood of the identity, has a dense conjugacy...
Jaroslav Nešetřil, Patrice Ossona de Mendez (2019)
Commentationes Mathematicae Universitatis Carolinae
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global convergence to graphs with unbounded degrees. As an application, we extend previous results on continuous clustering of local convergent sequences and prove the existence of modeling quasi-limits for local-global convergent sequences of nowhere dense graphs.
Shichang Song (2013)
Fundamenta Mathematicae
We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.
Klaas Pieter Hart, B. J. van der Steeg (2002)
Acta Universitatis Carolinae. Mathematica et Physica
Stanisław Kasjan (2002)
Fundamenta Mathematicae
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
Omer Angel, Alexander S. Kechris, Russell Lyons (2014)
Journal of the European Mathematical Society
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
Marek Cúth (2012)
Fundamenta Mathematicae
We simplify the presentation of the method of elementary submodels and we show that it can be used to simplify proofs of existing separable reduction theorems and to obtain new ones. Given a nonseparable Banach space X and either a subset A ⊂ X or a function f defined on X, we are able for certain properties to produce a separable subspace of X which determines whether A or f has the property in question. Such results are proved for properties of sets: of being dense, nowhere dense, meager, residual...
Ljiljana Petrović, Sladjana Dimitrijević (2011)
Czechoslovak Mathematical Journal
In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept...
Wojciech Stadnicki (2012)
Colloquium Mathematicae
We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
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