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The Field of Reals is not omega-Automatic

Authors Faried Abu Zaid, Erich Grädel, Lukasz Kaiser



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Author Details

Faried Abu Zaid
Erich Grädel
Lukasz Kaiser

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Faried Abu Zaid, Erich Grädel, and Lukasz Kaiser. The Field of Reals is not omega-Automatic. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 577-588, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.577

Abstract

We investigate structural properties of omega-automatic presentations of infinite structures in order to sharpen our methods to determine whether a given structure is omega-automatic. We apply these methods to show that no field of characteristic 0 admits an injective omega-automatic presentation, and that uncountable fields with a definable linear order cannot be omega-automatic.
Keywords
  • Logic
  • Algorithmic Model Theory
  • Automatic Structures

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