DeepAI AI Chat
Log In Sign Up

Congruence Preservation, Lattices and Recognizability

04/13/2020
by   Patrick Cegielski, et al.
UPEC
IRIF
0

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave like the operations of the algebra. The first way is to preserve congruences or stable preorders. The second way is to demand that preimages of recognizable sets belong to the lattice or the Boolean algebra generated by the preimages of recognizable sets by derived unary operation of the algebra (such as translations, quotients,. . . ).

READ FULL TEXT

page 1

page 2

page 3

page 4

05/19/2019

About a 'concrete' Rauszer Boolean algebra generated by a preorder

Inspired by the fundamental results obtained by P. Halmos and A. Monteir...
05/08/2023

Preservation theorems for Tarski's relation algebra

We investigate a number of semantically defined fragments of Tarski's al...
04/30/2019

Overlap Algebras: a constructive look at complete Boolean algebras

The notion of a complete Boolean algebra, although completely legitimate...
09/05/2019

Connected monads weakly preserve products

If F is a (not necessarily associative) monad on Set, then the natural t...
12/30/2020

Commutative Information Algebras: Representation and Duality Theory

Information algebras arise from the idea that information comes in piece...
05/05/2020

A Linear Algebra Approach to Linear Metatheory

Linear typed λ-calculi are more delicate than their simply typed sibling...
06/19/2020

Graphs with Multiple Sources per Vertex

Several attempts have been made at constructing Abstract Meaning Represe...