Classical Predicative Logic-Enriched Type Theories
Journal article, 2010
The two LTTs we construct are subsystems of the logic-enriched type theory LTTW, which is intended to formalise the classical predicative foundation presented by Herman Weyl in his monograph Das Kontinuum. The system has also been claimed to correspond to Weyl’s foundation. By casting ACA0 and ACA as LTTs, we are able to compare them with LTTW. It is a consequence of the work in this paper that LTTW is strictly stronger than ACA0.
The conservativity proof makes use of a novel technique for proving one LTT conservative over another, involving defining an interpretation of the stronger system out of the expressions of the weaker. This technique should be applicable in a wide variety of different cases outside the present work.
second order arithmetic
logic-enriched type theory
Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)
Royal Holloway University of London
Annals of Pure and Applied Logic
0168-0072 (ISSN)Vol. 161 11 1315-1345
Algebra and Logic