A generalization of the Takeuti-Gandy interpretation

Journal article, 2015

We present an interpretation of a version of dependent type theory where a type is interpreted by a Kan semisimplicial set. This interprets only a weak notion of conversion similar to the one used in the first published version of Martin-Lof type theory. Each truncated version of this model can be carried out internally in dependent type theory, and we have formalized the first truncated level, which is enough to represent isomorphisms of algebraic structure as equality.