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

Archive for Mathematical Logic 41 (3):251-257 (2002)
  Copy   BIBTEX


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="" Mathematics Subject Classification (2000): 03B30, 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



    Upload a copy of this work     Papers currently archived: 76,442

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Variations on a theme by Weiermann.Toshiyasu Arai - 1998 - Journal of Symbolic Logic 63 (3):897-925.
Unary primitive recursive functions.Daniel E. Severin - 2008 - Journal of Symbolic Logic 73 (4):1122-1138.
Finitary Set Theory.Laurence Kirby - 2009 - Notre Dame Journal of Formal Logic 50 (3):227-244.
Ramsey's Theorem for Pairs and Provably Recursive Functions.Alexander Kreuzer & Ulrich Kohlenbach - 2009 - Notre Dame Journal of Formal Logic 50 (4):427-444.
Anti-admissible sets.Jacob Lurie - 1999 - Journal of Symbolic Logic 64 (2):407-435.
Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.
The Ackermann functions are not optimal, but by how much?H. Simmons - 2010 - Journal of Symbolic Logic 75 (1):289-313.
Decidability of ∃*∀∀-sentences in HF.D. Bellè & F. Parlamento - 2008 - Notre Dame Journal of Formal Logic 49 (1):55-64.
Fragments of $HA$ based on $\Sigma_1$ -induction.Kai F. Wehmeier - 1997 - Archive for Mathematical Logic 37 (1):37-49.
A generalization of the limit lemma and clopen games.Peter Clote - 1986 - Journal of Symbolic Logic 51 (2):273-291.


Added to PP

30 (#392,052)

6 months
1 (#454,876)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

A variant to Hilbert's theory of the foundations of arithmetic.G. Kreisel - 1953 - British Journal for the Philosophy of Science 4 (14):107-129.

Add more references