Many-Sorted Equivalence of Shiny and Strongly Polite Theories

Herein we close the question of the equivalence of shiny and strongly polite theories by establishing that, for theories with a decidable quantifier-free satisfiability problem, the set of many-sorted shiny theories coincides with the set of many-sorted strongly polite theories. Capitalizing on this equivalence, we obtain a Nelson–Oppen combination theorem for many-sorted shiny theories.

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