Extending Martin-Löf Type Theory by one Mahlo-universe

We deene a type theory MLM, which has proof theoretical strength slightly greater then Rathjens theory KPM. This is achieved by replacing the universe in Martin-LL of's Type Theory by a new universe V, which has the property that for every function f, mapping families of sets in V to families of sets in V, there exists a universe closed under f. We show that the proof theoretical strength of MLM is 1 M+!. Therefore we reach a strength slightly greater than jKPMj and V can be considered as a Mahlo-universe. Together with Se96a] it follows jMLMj = 1 ((M+!).