Related papers: Chain conditions in dependent groups
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 the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.
This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains.…
In the paper weak sufficient conditions for the reduction of the chain complex of a twisted product to a free finitely generated chain complex are found.
We prove tight closure analogues of results of Watanabe about chains and families of integrally closed ideals.
In this short note we show that if we add predicate for a dense complete indiscernible sequence in a dependent theory then the result is still dependent. This answers a question of Baldwin and Benedikt and implies that every unstable…
A necessary and sufficient condition is derived for the controllability of Kronecker product networks, where the factor networks are general directed graphs. The condition explicitly illustrates how the controllability of the factor…
We give a combinatorial description of the dg category of character sheaves on a complex reductive group $G$, extending results of [Li] for $G$ simply-connected. We also explicitly identify the parabolic induction/restriction functors.
Commensurable groups are bi-interpretable, under suitable definability conditions.
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…
Right feeble groups are defined as groupoids $(X,*)$ such that (i) $x, y\in X$ implies the existence of $a, b \in X$ such that $a*x = y$ and $b*y = x$. Furthermore, (ii) if $x, y, z \in X$ then there is an element $w\in X$ such that…
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite…
We introduce an Ulam-type stability condition for positive definite maps defined on a countable group and prove that this condition characterizes amenability.
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…
We prove an analogue of the fixed-point theorem for the case of definably amenable groups.
It is shown that finite groups in which the order of the product of every pair of elements of co-prime order is the product of the orders, is nilpotent.