## 2010.6: Remarks on $\Sigma$-definability without the equality test over the Reals

2010.6:
Andrei Morozov and Margarita Korovina
(2008)
*Remarks on $\Sigma$-definability without the equality test over the Reals.*
Electronic Notes in Theoretical Computer Science, 202.
pp. 305-313.
ISSN 1571-0661

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 234 Kb |

DOI: 10.1016/j.entcs.2008.03.023

## Abstract

In this paper we study properties of Σ–definability over the reals without the equality test which is one of the main concepts in the logical approach to computability over continuous data. It has been shown that a set $B\subset R^n$ is Σ–definable without the equality test if and only if $ B $ is c.e. open. If we allow the equality test, the structur$e of a Σ–definable subset of $R^n$ can be rather complicated. The next natural question to consider is the following. Is there an effective procedure producing a set which is a maximal c.e. open subset of a given Σ–definable with the equality subset of $R^n$? It this paper we give the negative answer to this question.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | CICADA, the real numbers Σ–definability, computably enumerable open sets |

Subjects: | MSC 2000 > 03 Mathematical logic and foundations MSC 2000 > 68 Computer science |

MIMS number: | 2010.6 |

Deposited By: | Dr Margarita Korovina |

Deposited On: | 08 January 2010 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item