Decidability of Scott's model as an ordered ℚ-vectorspace

Abstract

Let L = 〈<, +, hq, 1〉q∈ℚ where ℚ is the set of rational numbers and hq is a one-place function symbol corresponding to multiplication by q. Then the L-theory of Scott's model for intuitionistic analysis is decidable.

Encoding true second‐order arithmetic in the real‐algebraic structure of models of intuitionistic elementary analysis

“…Definition 4.1(3). To handle quantification over the natural numbers we shall use the L ‐definition of found in [2] (cf. § 5 below).…”

“…In the papers [11, 12], Scowcroft showed that the validity in the model of certain ‐sentences of the language L of ordered rings is also decidable. We proved the decidability of Scott's model restricted to the language of ordered ‐vectorspaces in [2] and that proof indeed used, via Rabin's theorem, the decidability of the underlying topological structure. But the full real algebraic structure turned out to be undecidable.…”

Undecidability of the Real‐Algebraic Structure of Scott's Model

“…In [5] he showed that the universal fragment of the order structure is decidable. Other decidable fragments of the model were described in the papers of SCOWCROFT ( [6] and [7]) and in [2]. These results led to decidability results in the constructive and intuitionistic theory of reals (cf.…”