info:eu-repo/semantics/article
A note on chain-based semi-Heyting algebras
Fecha
2020-12Registro en:
Cornejo, Juan Manuel; Monteiro, Luiz F.; Sankappanavar, Hanamantagouda P.; Viglizzo, Ignacio Dario; A note on chain-based semi-Heyting algebras; Wiley VCH Verlag; Mathematical Logic Quarterly; 66; 4; 12-2020; 409-417
0942-5616
CONICET Digital
CONICET
Autor
Cornejo, Juan Manuel
Monteiro, Luiz F.
Sankappanavar, Hanamantagouda P.
Viglizzo, Ignacio Dario
Resumen
We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non-isomorphic semi-Heyting chains of a given size in some important subvarieties of the variety of semi-Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers (,) of non-isomorphic semi-Heyting chains with n elements such that removing the mth element ( 1<< ) we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi-Heyting chain with −1 elements can be extended to a n element semi-Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers (,) that provides some extra information.