  Let us denote by LF the class of all orthomodular lattices (OMLs) that are
locally finite (i.e., L in LF provided each finite subset of L generates in L a
finite subOML). We first show in this note how one can obtain new locally
finite OMLs from the initial ones and enlarge thus the class LF . We find LF
considerably large though, obviously, not all OMLs belong to LF . We then study
states on the OMLs of LF . We show that local finiteness may to a certain
extent make up for distributivity. We for instance show that if L in LF and if
for any finite subOML K there is a state s : K to [0, 1] on K, then there is a
state on the entire L. We also consider further algebraic and state properties
of LF relevant to quantum logic theory.
