A Note on Congruences of Infinite Bounded Involution Lattices

We prove that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 its elements or equalling subsets, regardless whether it has as many ideals subsets. Furthermore, when they at most elements, these lattices algebras be chosen such all their preserve involutions, so reducts. Under the Generalized Continuum Hypothesis, this means ideals. Consequently, same holds for antiortholattices, a class paraorthomodular Brouwer-Zadeh lattices. Regarding shapes congruence lattice{ ordered in question, turns out that, long is not strictly larger than isomorphic to nonsingleton well-ordered set with largest element those cardinalities, provided join-irreducible case bounded lattice-ordered and, antiortholattices least 3 distinct predecessor join{irreducible, well; course, various constructions applied obtain different structures without changing cardinalities question. point sufficient conditions analogous results hold arbitrary variety.