Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-20T03:24:25.780Z Has data issue: false hasContentIssue false
  • English
  • Français

The effective content of surreal algebra

Published online by Cambridge University Press:  12 March 2014

Jacob Lurie
Jacob Lurie*
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 . 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 337 - 371
Copyright
Copyright © Association for Symbolic Logic 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Alling, Norman L., Foundations of analysis over surreal number fields, North Holland, Amsterdam, 1978.Google Scholar
[2] Berlekamp, Elwyn R. et al., Winning ways, vol. 1, Academic Press, London, 1982.Google Scholar
[3] Conway, John H., On numbers and games, Academic Press, London and New York, 1976.Google Scholar
[4] Gonshor, Harry, An introduction to the theory of surreal numbers, Cambridge University Press, Cambridge, 1986.Google Scholar
[5] Harkleroad, Leon, Recursive surreal numbers, Notre Dame Journal of Formal Logic, vol. 31 (1990), no. 3.Google Scholar
[6] Sacks, Gerald E., Higher recursion theory, Springer-Verlag, New York, 1990.Google Scholar