### arnold beckmann's pages

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

**File:** PDF-File

**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
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.