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We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
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