Dualities and Dual Pairs in Heyting Algebras

Foniok, Jan; Nešetřil, Jaroslav; Pultr, Aleš; Tardif, Claude

doi:10.1007/s11083-010-9163-3

Search citation statements

Order By: Relevance

Paper Sections

Select...

Homomorphism Order1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

2021

Publication Types

Select...

Other1

Article1

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact this characterization of dualities is of a categorical nature and it can be extended to the much more general situation of Heyting algebras [35].…”

Section: Homomorphism Ordermentioning

confidence: 99%

Sparse Combinatorial Structures: Classification and Applications

Nešetřil¹,

Mendez

2011

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)

Self Cite

View full text Add to dashboard Cite

We present results of the recent research on sparse graphs and finite structures in the context of contemporary combinatorics, graph theory, model theory and mathematical logic, complexity of algorithms and probability theory. The topics include: complexity of subgraph-and homomorphism-problems; model checking problems for first order formulas in special classes; property testing in sparse classes of structures. All these problems can be studied under the umbrella of classes of structures which are Nowhere Dense and in the context of Nowhere Dense-Somewhere Dense dichotomy. This dichotomy presents the classification of the general classes of structures which proves to be very robust and stable as it can be defined alternatively by most combinatorial extremal invariants as well as by algorithmic and logical terms. We give examples from logic, geometry and extremal graph theory. Finally we characterize the existence of all restricted dualities in terms of limit objects defined on the homomorphism order of graphs.

show abstract

“…In fact this characterization of dualities is of a categorical nature and it can be extended to the much more general situation of Heyting algebras [35].…”

Section: Homomorphism Ordermentioning

confidence: 99%