Heyting*algebras, topological boolean algebras and P.O. systems
β Scribed by Alain Touraille
- Publisher
- Springer
- Year
- 1987
- Tongue
- English
- Weight
- 607 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0002-5240
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π SIMILAR VOLUMES
In classes of algebras such as lattices, groups, and rings, there arefinite algebras which individually generate quasivarieties which are not finitely axiomatiza.ble (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras
## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x β¬ C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,
In this paper, we will give a general description of subdirectly irreducible Heyting algebras with operators under some weak conditions, which includes the finite case, the normal case and the case for Boolean algebras with diamond operator. This can be done by normalizing these operators. This answ