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The Effective Content of Surreal Algebra

Jacob Lurie

The Journal of Symbolic Logic

Vol. 63, No. 2 (Jun., 1998), pp. 337-371

Published by: Association for Symbolic Logic

DOI: 10.2307/2586835

Stable URL: http://www.jstor.org/stable/2586835

Page Count: 35

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The Effective Content of Surreal Algebra

Abstract

This paper defines and explores the properties of several effectivizations of the structure of surreal numbers. The construction of one of previously investigated systems, the metadyadics, is shown to be effectively equivalent to the construction of the surreals in L_ω₁CK. This equivalence is used to answer several open questions concerning the metadyadics. Results obtained seem to indicate that the metadyadics best capture the notion of a recursive surreal number.

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