March 2012 Normal forms for elementary patterns
Timothy J. Carlson, Gunnar Wilken
J. Symbolic Logic 77(1): 174-194 (March 2012). DOI: 10.2178/jsl/1327068698


A notation for an ordinal using patterns of resemblance is based on choosing an isominimal set of ordinals containing the given ordinal. There are many choices for this set meaning that notations are far from unique. We establish that among all such isominimal sets there is one which is smallest under inclusion thus providing an appropriate notion of normal form notation in this context. In addition, we calculate the elements of this isominimal set using standard notations based on collapsing functions. This provides a capstone to the results in [2, 6, 8, 9, 7], using further refinement of ordinal arithmetic developed in [8] which then both allows for a simple characterization of normal forms for patterns of order one and will play a key role in the arithmetical analysis of pure patterns of order two, [5].


Download Citation

Timothy J. Carlson. Gunnar Wilken. "Normal forms for elementary patterns." J. Symbolic Logic 77 (1) 174 - 194, March 2012.


Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1275.03154
MathSciNet: MR2951636
Digital Object Identifier: 10.2178/jsl/1327068698

Keywords: algorithms , ordinal arithmetic , ordinal notations , patterns of resemblance , proof theory

Rights: Copyright © 2012 Association for Symbolic Logic


This article is only available to subscribers.
It is not available for individual sale.

Vol.77 • No. 1 • March 2012
Back to Top