Sergei Tupailo

	Finitary reductions for local predicativity, II:
		  recursively Mahlo ordinals


We will present a method of extracting finitary reductions for a
theory stating existence of recursively Mahlo ordinals. The method is
the same as for a theory of strength of ID_1, presented at this
seminar last quarter

(see http://www-logic.stanford.edu/Abstracts/Seminar/021798 ),

but of course presence of Mahlo makes proof-theoretical analysis
itself (by either infinitary or finitary approach) more involved.  Our
treatment of infinitary variant of the theory essentially follows
M. Rathjen's analysis of KPM [Ra91].

Since extracting finitary reductions follows completely standard
method and was presented by G. Mints at last seminar and ourselves on
February 24 in some detail, we will not talk much about it but only
outline some general features involved there.


REFERENCES

[Ar97] T. Arai. Proof theory for theories of ordinals,
I-III. Preprints, 1996-97

[Ra91] M. Rathjen. Proof theoretic analysis of KPM. Arch. Math. Logic,
30:377-403, 1991

[Tu98] S. Tupailo. Finitary reductions for local
predicativity. Preprint, 1998