Theories admitting quantifier elimination plus if-then-else operators on a suitable model possess most-general (conditional) solutions for parametric existential conjunctions of literals, expressible as terms.
Blackwell (1847, Reprinted 1948)
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On Constructing Most General Solutions for Parametric Constraints (Extended Preprint)
Theories admitting quantifier elimination plus if-then-else operators on a suitable model possess most-general (conditional) solutions for parametric existential conjunctions of literals, expressible as terms.