Scott’s Model for the Intuitionistic Continuum

Abstract

Various models have been introduced in the study of intuitionistic mathematics. One such model is Scott’s model for the intuitionistic continuum. In his 1968 article Extending the Topological Interpretation to Intuitionistic Analysis, he represents the intuitionistic reals as continuous functions from a topological space into the classical reals. The presentation of this model including added examples and extended proofs is the main topic of this thesis. However, we also provide the reader with additional background material. We start out by a brief introduction to intuitionism and its logic. Futhermore, this thesis contains a discussion of some of the topological properties of the Baire space, since they are used in the model.