The lattice of congruences of a finite line frame
![Thumbnail](/bitstream/handle/11086/552149/1504_01789.pdf.jpg?sequence=4&isAllowed=y)
View/ Open
Date
2017Author
Areces, Carlos Eduardo
Campercholi, Miguel Alejandro Carlos
Penazzi, Daniel Eduardo
Sánchez Terraf, Pedro Octavio
ORCID
https://orcid.org/0000-0001-7845-8503https://orcid.org/0000-0003-1166-1421
https://orcid.org/0000-0003-3928-6942
Metadata
Show full item recordAbstract
Let F = <F, R> be a finite Kripke frame. A congruence of F is a bisimulation of F that is also an equivalence relation on F. The set of all congruences of F is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that F is a finite line frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence ρ, the interval [IdF , ρ] embeds into the lattice of divisors of a suitable positive integer. We also prove that any two congruences with a nontrivial upper bound permute.