Taking the path computably traveled-Reference-Cited by-同舟云学术

Taking the path computably traveled

Published:2019-08-23 Issue:6 Volume:29 Page:969-973
ISSN:0955-792X
Container-title:Journal of Logic and Computation
language:en
Short-container-title:

Author:

Franklin Johanna N Y¹,Turetsky Dan²

Affiliation:

1. Department of Mathematics Room 306, Roosevelt Hall Hofstra University Hempstead, NY USA

2. Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand

Abstract

Abstract We define a real $A$ to be low for paths in Baire space (or Cantor space) if every $\varPi ^0_1$ class with an $A$-computable element has a computable element. We prove that lowness for paths in Baire space and lowness for paths in Cantor space are equivalent and, furthermore, that these notions are also equivalent to lowness for isomorphism.

Publisher

Oxford University Press (OUP)

Subject

Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science

Link

http://academic.oup.com/logcom/article-pdf/29/6/969/31910387/exz016.pdf

Reference8 articles.

1. Algorithmic Randomness and Complexity

2. Degrees that are low for isomorphism;Franklin;Computability,2014

3. Lowness for isomorphism and degrees of genericity;Franklin;Computability,2018

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