Valuations and Dedekindʹs Prague Theorem

To any field K we associate an entailment relation in the sense of Scott (Proceedings of the Tarski Symposium, 1974, pp. 411–435). In this way we can interpret an abstract propositional theory representing a generic valuation ring of a field, and obtain a simple effective proof of Dedekindʹs Prague theorem (Edwards, Arch. Hist. Ex. Sci (1980) 321–378; Divisor Theory, Birkhäuser, Boston, 1990).