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We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third…
We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).
We prove that the tree independence number of every even-hole-free graph is at most polylogarithmic in its number of vertices. More explicitly, we prove that there exists a constant c>0 such that for every integer n>1 every n-vertex…
We study a general Scalar-Tensor Theory with an arbitrary coupling funtion $\omega (\phi )$ but also an arbitrary dependence of the ``gravitational constant'' $G(\phi )$ in the cases in which either one of them, or both, do not admit an…
We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets…
In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency…
We study expansions of NSOP$_1$ theories that preserve NSOP$_1$. We prove that if $T$ is a model complete NSOP$_1$ theory eliminating the quantifier $\exists^{\infty}$, then the generic expansion of $T$ by arbitrary constant, function, and…
We initiate the study of a generalization of Kim-independence, Conant-independence, based on the "strong Kim-dividing" of Kaplan, Ramsey and Shelah. We introduce an axiom on stationary independence relations essentially generalizing the…
We give several new characterizations of $IP$ (the independence property) and $SOP$ (the strict order property) for continuous first order logic and study their relations to the function theory and the Banach space theory. We suggest new…
We study the theory $T_{m,n}$ of existentially closed incidence structures omitting the complete incidence structure $K_{m,n}$, which can also be viewed as existentially closed $K_{m,n}$-free bipartite graphs. In the case $m = n = 2$, this…
We show that for any $n\geq 3$ the theory of open generalized $n$-gons is complete, decidable and strictly stable, yielding a new class of examples in the zoo of stable theories.
The main purpose of this paper is to present a new and more uniform model-theoretic/combinatorial proof of the theorem ([5]): The randomization $T^{R}$ of a complete first-order theory $T$ with $NIP$ is a (complete) first-order continuous…
We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
This article gives a concise overview of the development and current status of studies on healthy models of the early Universe without an initial singularity, namely the cosmological bounce and Genesis scenarios, constructed within a broad…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several…
We develop the theory of Kim-independence in the context of NSOP$_{1}$ theories satsifying the existence axiom. We show that, in such theories, Kim-independence is transitive and that $\ind^{K}$-Morley sequences witness Kim-dividing. As…
We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other…