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The complexity of sets

André Nies

in Computability and Randomness

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies the complexity of sets of natural numbers. There are two interrelated types of complexity, these are computational and descriptive. In both cases, to understand the complexity of ... More


Some advanced computability theory

André Nies

in Computability and Randomness

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter develops the language of building Turing functionals which is used to characterize promptly simple degrees by low cuppability, and to prove the pseudo-jump inversion theorem of Jockusch ... More


Computability and Randomness

André Nies

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199230761
eISBN:
9780191710988
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230761.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic ... More


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