Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach

We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial ⁴. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between localized exotic small R ⁴'s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R ⁴'s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means which may enforce a kind of decoherence.