TY - JOUR
AU - Celani, Sergio A.
AU - Montangie, Daniela
TI - <p>
HILBERT ALGEBRAS WITH A NECESSITY MODAL OPERATOR</p>
JF - Reports on Mathematical Logic
VL - 2014
PY - 2014
DO = 10.4467/20842589RM.14.004.2274
SN - 0137-2904
C1 - 2084-2589
SP - 47
EP - 77
N2 - <p style="text-align: justify;">
We introduce the variety of Hilbert algebras with a modal operator , called H-algebras. The variety of H-algebras is the algebraic counterpart of the f!;g-fragment of the intuitionitic modal logic IntK. We will study the theory of representation and we will give a topological duality for the variety of H-algebras. We are going to use these results to prove that the basic implicative modal logic IntK! and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of H-algebras.</p>
UR - https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/hilbert-algebras-with-a-necessity-modal-operator