Arnold Beckmann
Archive for Mathematical Logic 2002, Vol. 41, No. 3, pp. 251-257
Publication year: 2002

We show that there is a primitive recursive tree which is not well-founded, but which is well-founded for co-r.e. sets, provable in Σ_1-Ind. It follows that the supremum of order-types of primitive recursive well-orderings, whose well-foundedness on co-r.e. sets is provable in Σ_1-Ind, equals the limit of all recursive ordinals.