  In this paper (propositional) probability logic ($PL$) is investigated from
model theoretic point of view. First of all, the ultraproduct construction is
adapted for $\sigma$-additive probability models, and subsequently when this
class of models is considered it is shown that the compactness property holds
with respect to a fragment of $PL$ called basic probability logic ($BPL$). On
the other hand, when dealing with finitely-additive probability models, one may
extend the compactness property for a larger fragment of probability logic,
namely positive probability logic ($PPL$). We finally prove that while the
L\"owenheim-Skolem number of the class of $\sigma$-additive probability models
is uncountable, it is $\aleph_0$ for the class of finitely additive probability
models.
