Abstract
We construct by diagonalization a non-well-founded primitive recursive tree, which is well-founded for co-r.e. sets, provable in Σ1 0. 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 0, equals the limit of all recursive ordinals ω1 ck. RID=""ID="" <E5>Mathematics Subject Classification (2000): 03B30</E5>, 03F15 RID=""ID="" Supported by the Deutschen Akademie der Naturforscher Leopoldina grant #BMBF-LPD 9801-7 with funds from the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie. RID=""ID="" I would like to thank A. SETZER for his hospitality during my stay in Uppsala in December 1998 – these investigations are inspired by a discussion with him; S. BUSS for his hospitality during my stay at UCSD and for valuable remarks on a previous version of this paper; and M. MÖLLERFELD for remarks on a previous title.
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Received: 27 July 2000 / Published online: 25 February 2002
RID=""
ID="" <E5>Mathematics Subject Classification (2000): 03B30</E5>, 03F15
RID=""
ID="" Supported by the Deutschen Akademie der Naturforscher Leopoldina grant #BMBF-LPD 9801-7 with funds from the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie.
RID=""
ID="" I would like to thank A. SETZER for his hospitality during my stay in Uppsala in December 1998 – these investigations are inspired by a discussion with him; S. BUSS for his hospitality during my stay at UCSD and for valuable remarks on a previous version of this paper; and M. MÖLLERFELD for remarks on a previous title.
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Beckmann, A. A non-well-founded primitive recursive tree provably well-founded for co-r.e. sets . Arch. Math. Logic 41 , 251 –257 (2002). https://doi.org/10.1007/s001530100107
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DOI: https://doi.org/10.1007/s001530100107