Related papers: A Ramsey-Classification Theorem and its Applicatio…

We prove general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado's Theorem by covering large classes of nonlinear equations. Sufficient conditions are obtained by…

Selective ultrafilters are characterized by many equivalent properties, in particular the Ramsey property that every finite colouring of unordered pairs of integers has a homogeneous set in U, and the equivalent property that every function…

In this paper we introduce a new topological Ramsey space whose elements are infinite ordered polyhedra. Then, we show as an application that the set of finite polyhedra satisfies two types of Ramsey property: one, when viewed as a category…

We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological…

In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natural isomorphism. We then proceed to Kan extend this…

We study families of infinite block sequences of elements of the space $\FIN_k$. In particular we study Ramsey properties of such families and Ramsey properties localized to a selective or semiselective coideal. We show how the stable…

We extend the formalism of Topological T-duality to spaces which are the total space of a principal $S^1$-bundle $p:E \to W$ with an $H$-flux in $H^3(E,Z)$ together the together with an automorphism of the continuous-trace algebra on $E$…

We prove a compactness theorem for full Boolean-valued models. As an application, we show that if $T$ is a complete countable theory and $\mathcal{B}$ is a complete Boolean algebra, then $\lambda^+$-saturated $\mathcal{B}$-valued models of…

For each finite semisimple tensor category, we associate a quantum group (face algebra) whose comodule category is equivalent to the original one, in a simple natural manner. To do this, we also give a generalization of the Tannaka-Krein…

We extend Makkai duality between coherent toposes and ultracategories to a duality between toposes with enough points and ultraconvergence spaces. Our proof generalizes and simplifies Makkai's original proof. Our main result can also be…

Ramsey algebras are algebras that induce Ramsey spaces, which are generalizations of the Ellentuck space and Milliken's space. Previous work suggests a possible local version of Ramsey algebras induced by infinite sequences. Hence, we…

A rank-three tensor model in canonical formalism has recently been proposed. The model describes consistent local-time evolutions of fuzzy spaces through a set of first-class constraints which form an on-shell closed algebra with structure…

We show that every free amalgamation class of finite structures with relations and (symmetric) partial functions is a Ramsey class when enriched by a free linear ordering of vertices. This is a common strengthening of the…

We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here…

Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…

We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of…

In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are…

We characterize the Tukey order, the Galvin property/ Cohesive ultrafilters from \cite{Kanamori1978} in terms of ultrapowers. We use this characterization to measure the distance between the Tukey order and other well-known orders of…

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$-manifolds whose coefficient systems are $n$-disk algebras or $n$-disk stacks. In this work we…

Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising…