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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