The elementary theory of interval real numbers. (English) Zbl 0547.03007
R. E. Moore [Interval analysis (1966; Zbl 0176.133)] introduced a model \({\mathcal I}({\mathbb{R}})\) for the ”real numbers” whose elements are compact real intervals. In this paper the first-order theory of \({\mathcal I}({\mathbb{R}})\) is axiomatized and Tarski’s quantifier elimination method for real closed fields is modified to show that the elementary theory of \({\mathcal I}({\mathbb{R}})\) is decidable.
MSC:
03B25 | Decidability of theories and sets of sentences |
03C10 | Quantifier elimination, model completeness, and related topics |
68P05 | Data structures |
06F99 | Ordered structures |