We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
Gli insiemi parziali sono coppie di sottoinsiemi di , dove . Gli insiemi parziali su costituiscono una DMF-algebra, ossia un'algebra di De Morgan in cui la negazione ha un solo punto fisso. Dimostriamo che ogni DMF-algebra è isomorfa a un campo di insiemi parziali. Utilizzando gli insiemi parziali su come aperti, introduciamo il concetto di spazio topologico parziale su . Infine associamo ad ogni DMF-algebra uno spazio topologico parziale i cui clopen compatti costituiscono un campo d'insiemi...
We modify slightly the definition of -partial functions given by Celani and Montangie (2012); these partial functions are the morphisms in the category of -space and this category is the dual category of the category with objects the Hilbert algebras with supremum and morphisms, the algebraic homomorphisms. As an application we show that finite pure Hilbert algebras with supremum are determined by the monoid of their endomorphisms.
In this note we describe the structure of dually residuated -monoids (-monoids) that have no non-trivial convex subalgebras.