In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality $n$, where $n$ is any natural number $ > 0$. The basic idea in the proof is to apply the notion of companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above.
"Uncompactness of Stit Logics Containing Generalized Refref Conditionals." Notre Dame J. Formal Logic 39 (4) 485 - 506, Fall 1998. https://doi.org/10.1305/ndjfl/1039118864