Abstract.
We will introduce a partial ordering \(\preceq_1\) on the class of ordinals which will serve as a foundation for an approach to ordinal notations for formal systems of set theory and second-order arithmetic. In this paper we use \(\preceq_1\) to provide a new characterization of the ubiquitous ordinal \(\epsilon _{0}\).
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Received: 18 August 1997
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Carlson, T. Ordinal arithmetic and \(\Sigma_{1}\)-elementarity. Arch Math Logic 38, 449–460 (1999). https://doi.org/10.1007/s001530050150
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DOI: https://doi.org/10.1007/s001530050150