Related papers: Homomorphism Preservation Theorems for Many-Valued…

We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

Conservative constraint satisfaction problems (CSPs) constitute an important particular case of the general CSP, in which the allowed values of each variable can be restricted in an arbitrary way. Problems of this type are well studied for…

We develop a Witt--Hadamard calculus for Euler products that unifies the classical Gauss congruences with their modern refinement, the Dold congruences. Within this framework we prove \emph{norm descent}: Dold congruences are functorial…

We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type theory. An infinity group is simply the loops in a pointed, connected type, where the group structure comes from the…

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…

The aims of this paper are to answer several conjectures and questions about multiplier spectrum of rational maps and to give new proofs of several rigidity theorems in complex dynamics, by combining tools from complex and non-archimedean…

The celebrated Trakhtenbrot's theorem states that the set of finitely valid sentences of first-order logic is not computably enumerable. In this note we will extend this theorem by proving that the finite satisfiability problem of any…

We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of fundamental groups, for which we obtain a more…

The aim of homotopy theory in topology is to simplify, after continuous deformation, continuous maps between topological spaces. What prevents this from happening are homotopy invariants. This raises quantitative questions: $\bullet$ Is the…

Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…

We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism…

We generalize pp elimination for modules, or more generally abelian structures, to a continuous logic environment where the abelian structure is equipped with a homomorphism to a compact (Hausdorff) group. We conclude that the continuous…

We show how topological methods developed in a previous article can be applied to prove new results about topological and homological finiteness properties of monoids. A monoid presentation is called special if the right-hand side of each…

The Constraint Satisfaction Problem (CSP) is a problem of computing a homomorphism $\mathbf{R}\to \mathbf{\Gamma}$ between two relational structures, where $\mathbf{R}$ is defined over a domain $V$ and $\mathbf{\Gamma}$ is defined over a…

This article supplements recent work of the authors. (1) A criterion for failure of covariant finiteness of a full subcategory of $\Lambda\text{-mod}$ is given, where $\Lambda$ is a finite dimensional algebra. The criterion is applied to…

(CROPPED TO FIT IN ARXIV'S SILLY LIMIT. SEE PDF FOR COMPLETE ABSTRACT.) We are the first to thoroughly explore a large space of formal secure compilation criteria based on robust property preservation, i.e., the preservation of properties…

Canonical formulation of higher order theory of gravity can only be accomplished associating additional degrees of freedom, which are extrinsic curvature tensor. Consequently, to match Cauchy data with the boundary data, terms in addition…

We classify the homogeneous finite-dimensional permutation structures, i.e., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification…