Archive for Mathematical Logic

, Volume 39, Issue 3, pp 155–181 | Cite as

Extending Martin-Löf Type Theory by one Mahlo-universe

  • Anton Setzer


We define a type theory MLM, which has proof theoretical strength slightly greater then Rathjen's theory KPM. This is achieved by replacing the universe in Martin-Löf's Type Theory by a new universe V having the property that for every function f, mapping families of sets in V to families of sets in V, there exists a universe inside V closed under f. We show that the proof theoretical strength of MLM is \(\geq \psi_{\Omega_1}\Omega_{{\rm M}+\omega}\). This is slightly greater than \(|{\rm KPM}|\), and shows that V can be considered to be a Mahlo-universe. Together with [Se96a] it follows \(|{\rm MLM}|=\psi_{\Omega_1}(\Omega_{{\rm M}+\omega})\).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Anton Setzer
    • 1
  1. 1.Department of Mathematics, Uppsala University, P.O. Box 480, S-751 06 Uppsala, Sweden (e-mail: SE

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