Related papers: On generically stable types in dependent theories

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

We initiate a systematic study of the class of theories without the tree property of the second kind - NTP2. Most importantly, we show: the burden is "sub-multiplicative" in arbitrary theories (in particular, if a theory has TP2 then there…

We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to…

We study generically stable measures in the local, NIP context. We show that in this setting, a measure is generically stable if and only if it admits a natural finite approximation.

We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…

The paper discusses from a metaphysical standpoint the nature of the dependence relation underpinning the talk of mutual action between material and spatiotemporal structures in general relativity. It is shown that the standard analyses of…

An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced…

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…

We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then…

Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…

We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…

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…

We present a type theory dealing with non-linear, "ordinary" dependent types (which we will call cartesian) and linear types, where both constructs may depend on terms of the former. In the interplay between these, we find new type formers…

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…

Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm{ACFG}$. This theory was introduced recently as a new example of $\mathrm{NSOP}_1$ non…

We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…