Results 111 to 120 of about 2,874 (140)

SYMMETRICAL HEYTING ALGEBRAS WITH OPERATORS

Mathematical Logic Quarterly, 1983
An algebra, \((A,+,\cdot,\to,\sim,0,1,S_ 1,...,S_{n-1}),\) \(n\geq 2\), is said to be a symmetrical Heyting algebra of order n \((SH_ n\)-algebra) if \((A,+,\cdot,\to,0,1)\) is a Heyting algebra, \((A,+,\cdot,\sim,0,1)\) is a de Morgan algebra and for all \(i,j=1,...,n-1\) and for \(x,y\in A: S_ i(x\cdot y)=S_ ix\cdot S_ iy, S_ i(x\to y)=\prod^{n- i}_ ...
openaire   +1 more source

Interpretations into Heyting algebras

Algebra Universalis, 1987
A variety \({\mathcal V}\) is interpretable in a variety \({\mathcal W}\) if for each \({\mathcal V}\)-operation \(F_ t(x_ 1,...,x_ n)\) there is a \({\mathcal W}\)- term \(f_ t(x_ 1,...,x_ n)\) such that if \((A;G_ s)\) is in \({\mathcal W}\), then \((A;f^ A_ t)\) is in \({\mathcal V}\).
openaire   +3 more sources

Boolean and Heyting Algebras

1993
In this chapter we discuss two well-known algebras as specially structured lattices and prove some of their properties as well as present some semantic interpretations of these structures.
Barbara H. Partee, Alice Ter Meulen, Robert E. Wall   +2 more
openaire   +1 more source

Expansions of Dually Pseudocomplemented Heyting Algebras

Studia Logica, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Heyting Algebras and Closure Algebras

2019
This chapter covers the fundamentals of Heyting algebras and closure algebras, as well as their connections to superintuitionistic logics and modal systems. Characterizations of the congruences of Heyting algebras and closure algebras are given in terms of filters and skeletal filters, respectively.
openaire   +1 more source

Characteristic Formulas of Partial Heyting Algebras

Logica Universalis, 2012
The notion of a characteristic (or Jankov) formula (introduced by \textit{V. A. Yankov} [Sov. Math., Dokl. 4, 1203--1204 (1963); translation from Dokl. Akad. Nauk SSSR 151, 1293--1294 (1963; Zbl 0143.25201)] is one of the very useful notions in the study of Heyting algebras.
openaire   +1 more source

The word problem for Heyting algebras

Algebra Universalis, 1987
A Heyting algebra with a unary operation \(a\mapsto a^*\) satisfying \(a\leq a^*\), \((a\cdot b)^*=a^*\cdot b^*\), and \((a\to b)^*\leq a+(a\to b)\) is called Heyting star algebra, or \(HA^*\) for short. Many properties of \(HA^*\)'s are inherited from their underlying Heyting algebras.
openaire   +1 more source

Free Heyting Algebras: Revisited

2009
We use coalgebraic methods to describe finitely generated free Heyting algebras. Heyting algebras are axiomatized by rank 0-1 axioms. In the process of constructing free Heyting algebras we first apply existing methods to weak Heyting algebras--the rank 1 reducts of Heyting algebras--and then adjust them to the mixed rank 0-1 axioms.
Gehrke, M., Bezhanishvili, N.
openaire   +2 more sources

Heyting* algebras, topological boolean algebras and P.O. systems

Algebra Universalis, 1987
The background to this paper is the theory of topological Boolean algebras (TBA's) developed by R. S. Pierce. TBA's are closure algebras with a unary operation which captures algebraic properties of the Cantor-Bendixson derivation. Using the notion of Heyting algebras with a unary operation, also destined to capture algebraic properties of topological ...
openaire   +1 more source

Free and projective Heyting and monadic Heyting algebras

1995
Finitely generated Heyting algebras and monadic Heyting algebras are described in terms of perfect Kripke models using colouring technique. Defining projective algebras as retract of free algebras, the characteristic of finitely generated projective algebras is given in varieties of Heyting algebras and monadic Heyting algebras.
openaire   +1 more source