The amalgamation property (AP) is of particular interest in the study of residuated lattices due to its relationship with various syntactic interpolation properties of substructural logics. There are no examples to date of non-commutative varieties of residuated lattices that satisfy the AP. The variety SemRL of semilinear residuated lattices is a natural candidate for enjoying this property, since most varieties that have a manageable representation theory and satisfy the AP are semilinear. However, we prove that this is not the case, and in the process we establish that the same is true for the variety SemCanRL of semilinear cancellative residuated lattices. In addition, we prove that the variety whose members have a distributive lattice reduct and satisfy the identity x(y∧z)w ≈ xyw∧xzw also fails the AP.

The failure of amalgamation property for semilinear varieties of residuated lattices

LEDDA, ANTONIO;
2015

Abstract

The amalgamation property (AP) is of particular interest in the study of residuated lattices due to its relationship with various syntactic interpolation properties of substructural logics. There are no examples to date of non-commutative varieties of residuated lattices that satisfy the AP. The variety SemRL of semilinear residuated lattices is a natural candidate for enjoying this property, since most varieties that have a manageable representation theory and satisfy the AP are semilinear. However, we prove that this is not the case, and in the process we establish that the same is true for the variety SemCanRL of semilinear cancellative residuated lattices. In addition, we prove that the variety whose members have a distributive lattice reduct and satisfy the identity x(y∧z)w ≈ xyw∧xzw also fails the AP.
File in questo prodotto:
File Dimensione Formato  
08_637-13_Gil-Led-Tsin.pdf

Solo gestori archivio

Tipologia: versione pre-print
Dimensione 218.85 kB
Formato Adobe PDF
218.85 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/84773
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact