Related papers: Codensity, profiniteness and algebras of semiring-…
We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman's theorem states that they precisely specify pseudovarieties, i.e. classes of finite algebras closed under finite products,…
Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…
In previous articles, we showed that the category of profinite $L$-algebras (where $L$ is a normal modal logic with the finite model property) is monadic over $\textbf{Set}$. Then, we developed sequent calculi for extensions of the language…
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman's theorem states that they precisely specify pseudovarieties, i.e.~classes of finite algebras closed under finite products,…
Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having favourable categorical properties. Given a profinite ring…
Stone duality establishes a contravariant equivalence between the category of Boolean algebras and the category of compact, Hausdorff, totally disconnected topological spaces (Stone spaces). These spaces are precisely the profinite spaces…
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…
We determine the profinite completions of MV-algebras, and obtain a description that generalizes the well known profinite completions of Boolean algebras as the power sets of their Stone spaces. We also use the description found to…
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical…
Profinite algebras are the residually finite compact algebras; their underlying topological spaces are Stone spaces. We extend the theory of profinite algebras to a more general setting of Stone topological algebras. We introduce Stone…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…
For a commutative semiring S, by an S-algebra we mean a commutative semiring A equipped with a homomorphism from S to A. We show that the subvariety of S-algebras determined by the identities 1+2x=1 and x^2=x is closed under non-empty…
Let V be a normal affine variety over the real numbers R, and let S be a semi-algebraic subset of V(R). We study the subring B(S) of the coordinate ring of V consisting of the polynomials that are bounded on S. We introduce the notion of…
Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra.…
For G an arbitrary profinite group, we construct an algebraic model for rational G-spectra in terms of G-equivariant sheaves over the space of subgroups of G. This generalises the known case of finite groups to a much wider class of…
Profinite algebras are exactly those that are isomorphic to inverse limits of finite algebras. Such algebras are naturally equipped with Boolean topologies. A variety $\mathcal V$ is standard if every Boolean topological algebra with the…
In a previous paper, we showed that profinite $L$-algebras (where $L$ is a variety of modal algebras generated by its finite members) are monadic over $\mathbf{Set}$. This monadicity result suggests that profinite $L$-algebras could be…
Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…