Ordinal arithmetic and $\Sigma_{1}$ -elementarity

Archive for Mathematical Logic 38 (7):449-460 (1999)
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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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Citations of this work

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