Joaquim Reizi Higuchi

An Explicit Equational Schema for Joint Modal Validities

An explicit, computably enumerable infinite equational schema characterizes formulas valid both in the stated normal modal orthomodular class with Sasaki implication and in intuitionistic modal logic IK. The quantum class has a box preserving finite meets and the top element, wit...

A countable three-generated orthomodular lattice with no σ-complete embedding

We construct a countably infinite orthomodular lattice generated by three specified elements that has no bounded ortholattice embedding into any set-sized σ-complete orthomodular lattice. In particular, it has no embedding into any set-sized complete orthomodular lattice. The exa...