Related papers: Forcing in Ramsey theory
Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity.We show that these…
This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force-response relationship might be hard to specify exactly, although examples of forces and corresponding…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement set theory and lay out the necessary technical preliminaries.…
Cicho\'n's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's, Goldstern, Kellner and Shelah constructed a forcing…
Ramsey Theorem [6] for pairs is intuitionistically but not classically provable: it is equivalent to a subclassical principle [2]. In this note we show that Ramsey may be restated in an intuitionistically provable form, which is informative…
In the parlance of relational structures, the Finite Ramsey Theorem states that the class of all finite chains has the Ramsey property. A classical result of J. Ne\v{s}et\v{r}il and V. R\"{o}dl claims that the class of all finite posets…
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. This paper concerns specifically automatic structures over finite words and trees (ranked/unranked). We investigate the…
In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…
In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics. As an immediate consequence, it triggered a new interest for structural Ramsey theory. The purpose of…
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 prove a sharp structural result concerning finite colorings of pairs in well-founded trees.
We construct a Ramsey class whose objects are Steiner systems. In contrast to the situation with general $r$-uniform hypergraphs, it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose: one…
The inclusion of physical information in machine learning frameworks has revolutionized many application areas. This involves enhancing the learning process by incorporating physical constraints and adhering to physical laws. In this work…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
We show that the universal homogeneous partial order has finite big Ramsey degrees and discuss several corollaries. Our proof relies on parameter spaces and the Carlson-Simpson theorem rather than on (a strengthening of) the…