Related papers: Finite models, stability, and Ramsey's theorem
We introduce the category of structures and interpretations which allows us to discuss some issues of Grothendieck's anabelian geometry in model-theory terms. Our main result is a formulation in terms of pure stability theory of a problem…
We prove that double exponentiation is an upper bound to Ramsey theorem for colouring of pairs when we want to predetermine the order of the differences of successive members of the homogeneous set.
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special…
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely…
We deal with the systematic development of stability for the context of approximate elementary submodels of a monster metric space, which is not far, but still very distinct from the first order case. In particular we prove the analogue of…
We prove that for any choice of parameters $k,t,\lambda$ the class of all finite ordered designs with parameters $k,t,\lambda$ is a Ramsey class.
An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.
In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be…
Topological Ramsey spaces are spaces which support infinite dimensional Ramsey theory similarly to the Ellentuck space. Each topological Ramsey space is endowed with a partial ordering which can be modified to a $\sigma$-closed `almost…
We prove that the theory of abelian groups and R-modules even in infinitary logic is stable and understood to some extent.
Extending a result of K. Milliken \cite{Mi2}, in this paper we prove a Ramsey classification result for equivalence relations defined on uniform families of finite strong subtrees of a finite sequence $(U_i)_{i\in d}$ of fixed trees $U_i$,…
Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.
In contrast to the abundance of "direct" Ramsey results for classes of finite structures (such as finite ordered graphs, finite ordered metric spaces and finite posets with a linear extension), in only a handful of cases we have a…
This article discusses some recent trends in Ramsey theory on infinite structures. Trees and their Ramsey theory have been vital to these investigations. The main ideas behind the author's recent method of trees with coding nodes are…
We develop a transfer principle of structural Ramsey theory from finite structures to ultraproducts. We show that under certain mild conditions, when a class of finite structures has finite small Ramsey degrees, under the (Generalized)…
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and stability of the solution of generalized Dary-Forchheimer model.