Semi-Heyting Algebras Term Equivalent to Gödel Algebras

MANUEL ABAD; JOSÉ PATRICIO DÍAZ VARELA; JUAN MANUEL CORNEJO

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS

SPRINGER

Lugar: Berlin; Año: 2012 p. 1 - 18

0167-8094

In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety LH of Godel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety LCom of commutative semi-Heyting algebras and the variety Lsup generated by the chains in which a < b implies a-->b = b. We also study the variety C generated within SH by LH, Lsup and LCom. In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.