# The strength of some Martin-Löf type theories

@article{Griffor1994TheSO, title={The strength of some Martin-L{\"o}f type theories}, author={Edward R. Griffor and Michael Rathjen}, journal={Archive for Mathematical Logic}, year={1994}, volume={33}, pages={347-385} }

One objective of this paper is the determination of the proof-theoretic strength of Martin-Löf's type theory with a universe and the type of well-founded trees. It is shown that this type system comprehends the consistency of a rather strong classical subsystem of second order arithmetic, namely the one with Δ21 comprehension and bar induction. As Martin-Löf intended to formulate a system of constructive (intuitionistic) mathematics that has a sound philosophical basis, this yields a…

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