Well-ordering proofs for Martin-Löf Type Theory (1998)
| Venue: | Annals of Pure and Applied Logic |
| Citations: | 18 - 11 self |
BibTeX
@INPROCEEDINGS{Setzer98well-orderingproofs,
author = {Anton Setzer},
title = {Well-ordering proofs for Martin-Löf Type Theory},
booktitle = {Annals of Pure and Applied Logic},
year = {1998},
pages = {113--159}
}
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Abstract
We present well-ordering proofs for Martin-Lof'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 [Set93] show that the proof theoretical strength of the type theory is precisely ## 1# I+# , which is slightly more than the strength of Feferman's theory T 0 , classical set theory KPI and the subsystem of analysis (# 1 2 -CA)+(BI). The strength of intensional and extensional version, of the version a la Tarski and a la Russell are shown to be the same. 0 Introduction 0.1 Proof theory and Type Theory Proof theory and type theory have been two answers of mathematical logic to the crisis of the foundations of mathematics at the beginning of the century. Proof theory was originally established by Hilbert in order to prove the consistency of theories by using finitary methods. When Godel showed that Hilbert's program cannot be carried out as originally intended, the focus of proof theory ch...
