Presentation of the paper
Burešová, D.; Pták, P.
On locally finite orthomodular lattices
Mathematica Slovaca. 2023, 73(2), 545-549. DOI 10.1515/ms-2023-0040

Let us denote by LF the class of all orthomodular lattices (OMLs) that are
locally finite (i.e., L ∈ LF provided each finite subset of L generates in L
a
finite subOML). In this note, we first show 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. Then we study
states on the OMLs of LF. We show that local finiteness may to a certain extent
make up for distributivity. For instance, we show that if L ∈ LF and if for
any finite subOML K there is a state s: K → [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 the quantum logic theory.

Venue: The seminar will take place in Dejvice, JP3:B-600, and online through MS
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