A partial ordering P is chain-Ramsey if, for every natural number n and every coloring of the n-element chains from P in finitely many colors, there is a monochromatic subordering Q isomorphic to P. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a c...

This thesis investigates the interplay between two branches of discrete mathematics: Ramsey theory and random graphs. The origins of Ramsey theory can already be found in the work of Hilbert from the early 20th century. However, it was a simple but profound result of Frank P. Ramsey from 1930 which marked the beginning of the new field in mathematics. Phrased in graph theory terms, Ramsey’s the...

The Ramsey rule for the consumption rate of discount assumes a transfer of money of a (representative) agent at one point in time to the same agent at another point in time. Climate policy (implicitly) transfers money not just over time but also between agents. I propose three alternative modifications of the Ramsey rule to account for this. Taking the Ramsey rule as given, I derive an intuitiv...

Let C1 and C2 be strong amalgamation classes of finite structures, with disjoint finite signatures σ and τ . Then C1∧C2 denotes the class of all finite (σ∪τ)-structures whose σ-reduct is from C1 and whose τ -reduct is from C2. We prove that when C1 and C2 are Ramsey, then C1 ∧ C2 is also Ramsey. We also discuss variations of this statement, and give several examples of new Ramsey classes derive...

Set multipartite Ramsey numbers were introduced in 2004, generalizing the celebrated Ramsey numbers. Let C4 denote the four cycle and let K1,n denote the star on n + 1 vertices. In this paper we investigate bounds on C4−K1,n set multipartite Ramsey numbers. Relationships between these numbers and the classical C4−K1,n Ramsey numbers are explored. Then several near-optimal or exact classes are d...

We give a parametrization with perfect subsets of 2∞ of the abstract Ramsey theorem (see [13]). Our main tool is an adaptation, to a more general context of Ramsey spaces, of the techniques developed in [8] by J. G. Mijares in order to obtain the corresponding result within the context of topological Ramsey spaces. This tool is inspired by Todorcevic’s abstract version of the combinatorial forc...

For the standard one sector stochastic optimal growth model, we outline a new set of conditions for a policy function that satisfies the Ramsey-Euler equation to be optimal. An interior Ramsey-Euler policy function is optimal if (and only if) it is continuous or alternatively, if both consumption and investment are non-decreasing in output. One does not need to verify the transversality conditi...

We show that any finite affinely independent set can be isometrically embedded into a regular polygonal torus, is, the product of vertex sets some polygons. apply this result in context Euclidean Ramsey Theory, highlighting connection between two most significant results field which were previously thought to independent. In particular with straightforward application Kříž’s theorem we give an ...

This is a talk about the development of Ramsey theory, from combinatorial results like the classical pigeon hole principle, Ramsey’s theorem [14] and Hindman’s theorem [8], making emphasis in the notion of topological Ramsey space. In [6], Ellentuck gave a characterization of the Ramsey property which gave rise to the topological Ramsey theory. It was anticipated by the works of Nash-Williams [...