Related papers: Uniform Interpolation and Compact Congruences
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc closure(D) generated by z and h --- where h is a…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
We consider the closure space on the set of strings of a gentle algebra of finite representation type. Palu, Pilaud, and Plamondon proved that the collection of all biclosed sets of strings forms a lattice, and moreover, that this lattice…
It is well known that many geometric properties of Schubert varieties of type $A$ can be interpreted combinatorially. Given two permutations $w,x\in S_n$ we give a combinatorial consequence of the property that the smooth locus of the…
We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric…
In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
According to Lidstone interpolation theory, an entire function of exponential type $<\pi$ is determined by it derivatives of even order at $0$ and $1$. This theory can be generalized to several variables. Here we survey the theory for a…
We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…
We discuss conditions under which certain compactifications of topological spaces can be obtained by composing the ultrafilter space monad with suitable reflectors. In particular, we show that these compactifications inherit their…
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…
This paper shows that the sheaf representation of finitely presented Heyting algebras constructed by Ghilardi and Zawadowski is, from an algebraic perspective, equivalent to the construction of profinite completion. We show that the dual…
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
We generalize the results from "P. Lipparini, Productive $[\lambda,\mu]$-compactness and regular ultrafilters, Topology Proceedings, 21 (1996), 161--171"; in particular the present results apply to singular cardinals, too.
Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety $X$ always give the same value, when computed via the decomposition theorem on any…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties have never been treated individually, at least in a semantic…
In this paper, we study geometric properties of $\ell^{p}$-spaces associated with the unitary dual of a compact group. More precisely, we prove uniform smoothness, uniform convexity, Clarkson type inequalities, Kadec-Klee property, as well…