Related papers: Topological Ramsey Spaces Dense in Forcings
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
We introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, we propose a Tameness Conjecture that states that…
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.
Robinson spaces are structures equipped with a total order that encodes comparative dissimilarity relationships. We study the problem of representing Robinson dissimilarity spaces into low-dimensional metric spaces. These representations…
We introduce a ZFC method that enables us to build spaces (in fact special dense subspaces of certain Cantor cubes) in which we have "full control" over all dense subsets. Using this method we are able to construct, in ZFC, for each…
By a result of Zucker, every Fra\"iss\'e structure $\bf F$ for which the elements of $\mathrm{Age}(\bf F)$ have finite Ramsey degrees admits a Fra\"iss\'e precompact expansion $\bf F^{*}$ whose age $\mathrm{Age}(\bf F^{*})$ has the Ramsey…
We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop…
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Ne\v{s}et\v{r}il-R\"{o}dl Theorem, the author's Ramsey lift of bowtie-free graphs as well…
We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…
In this paper we first study the structure of the scalar and vector-valued nearly invariant subspaces with a finite defect. We then subsequently produce some fruitful applications of our new results. We produce a decomposition theorem for…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
Ramsey theory is the study of conditions under which mathematical objects show order when partitioned. Ramsey theory on the integers concerns itself with partitions of $[1,n]$ into $r$ subsets and asks the question whether one (or more) of…
We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization,…
Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper…
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as…