Well-ordering proofs for Martin-Löf type theory

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Abstract

We present well-ordering proofs for Martin-Löf's type theory with W-type and one universe. These proofs, together with an embedding of the type theory in a set theoretical system as carried out in Setzer (1993) show that the proof theoretical strength of the type theory is precisely ψΩ1Ω1 + ω, which is slightly more than the strength of Feferman's theory T0, classical set theory KPI and the subsystem of analysis (Δ12CA) + (BI). The strength of intensional and extensional version, of the version à la Tarski and à la Russell are shown to be the same.

MSC

03F03

MSC

03F50
03F15

Keywords

Martin-Löf's type theory
Intuitionistic type theory
Well-ordering proofs
Universe
W-type
Proof theory
KPI
T0
Ordinal analysis

Cited by (0)

Part of this research was done while the author was visiting the University of Leeds as part of the EC Twinning Project “Proofs and Computation”.