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A non-well-founded primitive recursive tree provably well-founded for co-r.e. sets

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Author: Arnold Beckmann
Title: A non-well-founded primitive recursive tree provably well-founded for co-r.e. sets
Journal: Archive for Mathematical Logic 2002, 41(3): 251-257
DOI: 10.1007/s001530100107

Abstract: 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 Σ1-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 Σ1-Ind , equals the limit of all recursive ordinals.

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