Related papers: Type decomposition in NIP theories

We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp.…

We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…

Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…

We give sufficient conditions for a predicate P in a complete theory T to be stably embedded: P with its induced 0-definable structure has "finite rank", P has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson and…

We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a…

Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable homotopy categories, stable module…

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.

We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting results of Glicksberg, we show that the supports of generically stable (or just definable,…

We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.

Let $K$ be a type-definable infinite field in an NIP theory. If $K$ has characteristic $p > 0$, then $K$ is Artin-Schreier closed (it has no Artin-Schreier extensions). As a consequence, $p$ does not divide the degree of any finite…

We give a construction of classifiers for double negation stable h-propositions in a variety of cubical set models of homotopy type theory and cubical type theory. This is used to give some relative consistency results: classifiers for…

We discuss two constructions for obtaining generically stable Keisler measures in an NIP theory. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable…

Various notions of dissipativity type for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case $L^p$-dissipativity. Most of the results are due to the authors.

Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a conjecture of Laskowski.

We present a new proof of descent for stably dominated types in any theory, dropping the hypothesis of the existence of global invariant extensions. Additionally, we give a much simpler proof of descent for stably dominated types in…

Let T be an NIP L-theory and T' be an enrichment. We give a sufficient condition on T' for the underlying L-type of any definable (respectively invariant) type over a model of T' to be definable (respectively invariant) as an L-type.…

We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…

We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology…

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 give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on…