A note on iterated consistency and infinite proofs.

Schmerl and Beklemishev's work on iterated reflection achieves two aims: it introduces the important notion of Π10-ordinal, characterizing the Π10-theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative calculus to compute the Π10-ordinals for a range of theories. The present note demonstrates that these achievements are independent: we read off Π10-ordinals from a Schütte-style ordinal analysis via infinite proofs, in a direct and transparent way. [ABSTRACT FROM AUTHOR]