Related papers: Forcing in Ramsey theory
I have two main aims. The first is general, and more philosophical (Section 2). The second is specific, and more closely related to physics (Sections 3 and 4). The first aim is to state my general views about laws and causation at different…
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cicho\'n diagram. First I…
We develop the theory of Fra\"iss\'e limits for classes of finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence of seminorms. We define a notion of a Fra\"iss\'e Fr\'echet space…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.
Diverse studies in systems neuroscience begin with extended periods of curriculum training known as `shaping' procedures. These involve progressively studying component parts of more complex tasks, and can make the difference between…
Reinforcement learning is one of the core components in designing an artificial intelligent system emphasizing real-time response. Reinforcement learning influences the system to take actions within an arbitrary environment either having…
F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to…
In this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK$^{**}$. We define this forcing by using a…
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,…
The potential lack of fairness in the outputs of machine learning algorithms has recently gained attention both within the research community as well as in society more broadly. Surprisingly, there is no prior work developing tree-induction…
We consider a Ramsey statement for pairs of maps between trees, where one is an embedding as defined by Deuber and the other is a rigid surjection as defined by Solecki. We show that there is no Ramsey Theorem for pairs of maps where the…
This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized…
We extend classical Flory-Rehner theory for the expansion and compression of porous materials such as cross-linked polymer networks. The theory includes volume exclusion, affinity with the solvent, and finite stretching of the polymer…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…
We survey results and open problems relating degree conditions with tree containment in graphs, random graphs, digraphs and hypergraphs, and their applications in Ramsey theory.
Inspired by the necessity of morphological adaptation in animals, a growing body of work has attempted to expand robot training to encompass physical aspects of a robot's design. However, reinforcement learning methods capable of optimizing…
When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments…