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Archive for Mathematical Logic

, Volume 41 , Issue 3 , pp 251 –257 | Cite as

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

  • Arnold Beckmann
  • 22 Downloads

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):&ensp;03B30</E5>, 03F15 RID=""ID="" Supported by the Deutschen Akademie der Naturforscher Leopoldina grant #BMBF-LPD 9801-7 with funds from the Bundesministerium f&uuml;r 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 &ndash; 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. M&Ouml;LLERFELD for remarks on a previous title.

Keywords

Subject Classification Previous Version Recursive Tree Recursive Ordinal Previous Title 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Arnold Beckmann
    • 1
  1. 1.Department of Mathematics, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA. e-mail: abeckman@math.ucsd.eduUS

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