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June 2007 Assignment of ordinals to patterns of resemblance
Gunnar Wilken
J. Symbolic Logic 72(2): 704-720 (June 2007). DOI: 10.2178/jsl/1185803630

Abstract

In [2] T. J. Carlson introduces an approach to ordinal notation systems which is based on the notion of Σ1-elementary substructure. We gave a detailed ordinal arithmetical analysis (see [7]) of the ordinal structure based on Σ1-elementarity as defined in [2]. This involved the development of an appropriate ordinal arithmetic that is based on a system of classical ordinal notations derived from Skolem hull operators, see [6]. In the present paper we establish an effective order isomorphism between the classical and the new system of ordinal notations using the results from [6] and [7]. Moreover, on the basis of a concept of relativization we develop mutual (relatively) elementary recursive assignments which are uniform with respect to the underlying relativization.

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Gunnar Wilken. "Assignment of ordinals to patterns of resemblance." J. Symbolic Logic 72 (2) 704 - 720, June 2007. https://doi.org/10.2178/jsl/1185803630

Information

Published: June 2007
First available in Project Euclid: 30 July 2007

zbMATH: 1121.03081
MathSciNet: MR2320297
Digital Object Identifier: 10.2178/jsl/1185803630

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 2 • June 2007
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