A Duality Theoretic View on Limits of Finite Structures

  title={A Duality Theoretic View on Limits of Finite Structures},
  author={Mai Gehrke and Tom'avs Jakl and Luca Reggio},
  journal={Foundations of Software Science and Computation Structures},
  pages={299 - 318}
A systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of measures arises — via Stone-Priestley duality and the notion of types from model theory — by enriching the expressive power of first-order… Expand
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
This work focuses on the use of topological duality methods and category theory and, more particularly, free (and co-free) constructions, to unify the `power' and `structure' strands in computer science. Expand


Unrestricted stone duality for Markov processes
This article considers an alternative definition of Aumann algebra that leads to dual adjunction for Markov processes that is aDuality for many measurable spaces occurring in practice and extends a duality for measurable spaces due to Sikorski. Expand
Duality and Equational Theory of Regular Languages
This paper presents a new result in the equational theory of regular languages, which emerged from lively discussions between the authors about Stone and Priestley duality, and shows for instance that any class ofregular languages defined by a fragment of logic closed under conjunctions and disjunctions admits an equational description. Expand
Representation of Distributive Lattices by means of ordered Stone Spaces
1. Introduction Stone, in [8], developed for distributive lattices a representation theory generalizing that for Boolean algebras. This he achieved by topologizing the set X of prime ideals of aExpand
A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional)Expand
Domain Theory in Logical Form
Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics, and the theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics are introduced. Expand
Canonical extensions of double quasioperator algebras: An algebraic perspective on duality for certain algebras with binary operations
Abstract The context for this paper is a class of distributive lattice expansions, called double quasioperator algebras (DQAs). The distinctive feature of these algebras is that their operationsExpand
Borel Structures for First-order and Extended Logics
Publisher Summary This chapter focuses on Borel structures for first-order and extended logics. The aspects of model theory to be discussed in this chapter blend together two general problems inExpand
Relating Structure and Power: Comonadic Semantics for Computational Resources - Extended Abstract
The results pave the way for systematic connections between two major branches of the field of logic in computer science which hitherto have been almost disjoint: categorical semantics, and finite and algorithmic model theory. Expand
The pebbling comonad in Finite Model Theory
It is shown that existential k-pebble games have a natural comonadic formulation and lays the basis for some new and promising connections between two areas within logic in computer science which have largely been disjoint: finite and algorithmic model theory, and semantics and categorical structures of computation. Expand
Duality for Double Quasioperator Algebras via their Canonical Extensions
It is shown that, for DQAs, generalized canonicity is sufficient to yield, in a uniform way, topological dualities in the same style as those for canonical varieties, however topology and correspondence are no longer separable in the the same way. Expand