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GENERICITY AND RANDOMNESS WITH ITTMS

Published online by Cambridge University Press:  09 September 2019

BENOÎT MONIN  and
PAUL-ELLIOT ANGLÈS D’AURIAC
BENOÎT MONIN
Affiliation:
LACL, DÉPARTEMENT D’INFORMATIQUE FACULTÉ DES SCIENCES ET TECHNOLOGIE 61 AVENUE DU GÉNÉRAL DE GAULLE 94010 CRÉTEIL CEDEX E-mail: benoit.monin@gmail.com
PAUL-ELLIOT ANGLÈS D’AURIAC
Affiliation:
LACL, DÉPARTEMENT D’INFORMATIQUE FACULTÉ DES SCIENCES ET TECHNOLOGIE 61 AVENUE DU GÉNÉRAL DE GAULLE 94010 CRÉTEIL CEDEX E-mail: peada@free.fr
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Abstract

We study genericity and randomness with respect to ITTMs, continuing the work initiated by Carl and Schlicht. To do so, we develop a framework to study randomness in the constructible hierarchy. We then answer several of Carl and Schlicht’s question. We also ask a new question one the equality of two classes of randoms. Although the natural intuition would dictate that the two classes are distinct, we show that things are not as simple as they seem. In particular we show that the categorical analogues of these two classes coincide, in contradiction with the natural intuition. Even though we are not able to answer the question for randomness in this article, we delineate and sharpen its contour and outline.

Keywords

03D60algorithmic randomnessITTMforcingconstructibleshigher computability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 4 , December 2019 , pp. 1670 - 1710
Copyright
Copyright © The Association for Symbolic Logic 2019 

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