Ordinal Arithmetic in I Δ0
Richard Sommer · 1993
Abstract We show that much of the basic theory of the ordinal functions and relations that are involved in proof-theoretic ordinal analysis, can be carried out in a very weak fragment of arithmetic, namely IΔ0, on an arbitrary recursive ordinal. General conditions are given for the Δ0-representability of ordinal relations and functions, and IΔ0-provability of their basic properties.