Normal forms for elementary patterns
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  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, .
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1327068698
Zentralblatt MATH identifier: 06025965
Mathematical Reviews number (MathSciNet): MR2951636
Digital Object Identifier: doi:10.2178/jsl/1327068698