Beth models of analysis are used in model theoretic proofs of the disjunction and existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

There is a model, for a system of intuitionistic analysis including Brouwer's principle for numbers and Kripke's schema, in which math formula ø-definable discrete sets of choice sequences are subcountable.

If one builds a topological model, analogous to that of Moschovakis , over the product of uncountably many copies of the Cantor set, one obtains a structure elementarily equivalent to Krol's model . In an intuitionistic metatheory Moschovakis's original model satisfies all the axioms of intuitionistic analysis, including the unrestricted version of weak continuity for numbers.

Based on the paper [4] we show that true second‐order arithmetic is interpretable over the real‐algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras.

We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.