摘要：We present a simple-to-state, abstract computational problem, whose solution implies the 1-consistency of various systems of predicative Analysis and offers a way of extracting witnesses from classical proofs. In order to state the problem, we formulate the concept of transfinite update procedure, which extends Avigad's notion of update procedure to the transfinite and can be seen as an axiomatization of learning as it implicitly appears in various computational interpretations of predicative Analysis. We give iterative and bar recursive solutions to the problem.
关键词：update procedure; epsilon substitution method; predicative classical analysis; bar recursion
