  This is a part of an ongoing research project, with the aim of finding the
connections between properties related to theory combination in Satisfiability
Modulo Theories. In previous work, 7 properties were analyzed: convexity,
stable infiniteness, smoothness, finite witnessability, strong finite
witnessability, the finite model property, and stable finiteness. The first two
properties are related to Nelson-Oppen combination, the third and fourth to
polite combination, the fifth to strong politeness, and the last two to
shininess. However, the remaining key property of shiny theories, namely, the
ability to compute the cardinalities of minimal models, was not yet analyzed.
In this paper we study this property and its connection to the others.
