Decidability of the elementary theory of universal semifields of the second kind (Q580393)

A universal semifield \(S_{\nabla}\) in the sense of \textit{M. Ya. Antonovskij}, \textit{V. G. Boltyanskij} and \textit{T. A. Sarymsakov} [Topological Boolean Algebras (Tashkent 1963; Zbl 0154.012)] is called a semifield of the second kind (or continuous) if the Boolean algebra \(\nabla\) is atom-free. Using a result of \textit{A. Macintyre} [Fundam. Math. 81, 73-89 (1973; Zbl 0317.02065)] the author proves that the theory of universal semifields of the second kind is decidable. He gives a system of axioms for such semifields.