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An upper bound for the provability of transfinite induction in systems with N-times iterated inductive definitions

  • W. Pohlers
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 500)

Abstract

The consistency of IDN is provable in IDN+transfinite induction up to ΘɛΩN+1O., hence this induction is not provable in IDN (and therefore also not provable in IDNi, the intuitionistic version.)

This follows from Theorems 1,2 and 3 since besides transfinite induction (and the provability predicate of IIN which is formalisable in IDN and even replaceable by a primitive recursive one) we only used finitary methods in our consistency proof.

Keywords

Weaken Part Inductive Definition Consistency Proof Logical Axiom Minimal Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • W. Pohlers

There are no affiliations available

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