Quasi-Heyting algebras: a new class of lattices (Q1264382)

Pastings of Boolean algebras along segments and embeddings (as weak as requested) into large Boolean algebras of such structures have long time been investigated. The author makes an attempt to give a definition generalizing orthomodular lattices and Heyting algebras by using Sasaki projections. The new structure is called QHA, short for quasi-Heyting algebras \(Q\). An additional arrow operation allows to prove for elements \(a\), \(b\) of \(Q\) that \(a\subset a\Rightarrow b\) and \(a\Rightarrow b= a\Rightarrow(a\wedge b)\).