Related papers: Lovely pairs for independence relations

We prove that for every simple theory $T$ (or even simple thick compact abstract theory) there is a (unique) compact abstract theory $T^\fP$ whose saturated models are the lovely pairs of $T$. Independence-theoretic results that were proved…

Let $T$ be a complete strongly geometric theory of fields with quantifier elimination. We show that the theory of lovely pairs of $T$ has quantifier elimination in Delon's definitional expansion by predicates for linear independence and…

We prove that the NTP$_1$ property of a geometric theory $T$ is inherited by theories of lovely pairs and $H$-structures associated to $T$. We also provide a class of examples of nonsimple geometric NTP$_1$ theories.

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

We prove that the definition of supersimplicity in metric structures from \cite{pezz:Morley} is equivalent to an \textit{a priori} stronger variant. This stronger variant is then used to prove that if $T$ is a supersimple Hausdorff cat then…

We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…

This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal structures, lovely pairs, fields with Mann groups, and…

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…

We show that the ample degree of a stable theory with trivial forking is preserved when we consider the corresponding theory of belles paires, if it exists. This result also applies to the theory of $H$-structures of a trivial theory of…

We develop a new notion of independence suggested by Scanlon (th-independence). We prove that in a large class of theories (which includes all simple theories) this notion has many of the properties needed for an adequate geometric…

We introduce an abstract framework to study certain classes of stably embedded pairs of models of a complete $\mathcal{L}$-theory $T$, called \textit{beautiful pairs}, which comprises Poizat's belles paires of stable structures and van den…

Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.

We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…

In this text we show, that the notion of a "good pair" that was introduced in the paper "Digital Manifolds and the Theorem of Jordan-Brouwer" has actually known models. We will show, how to choose cubical adjacencies, the generalizations of…

This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

In a previous paper we developed the notions of th-independence and \th-ranks which define a geometric independence relation in a class of theories which we called ``rosy''. We proved that rosy theories include simple and o-minimal theories…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…

We derive a simple mathematical "theory" to show that two decision-making entities can work better together only if at least one of them is occasionally willing to stay neutral. This provides a mathematical "justification" for an age-old…