Author:
BIENVENU LAURENT,CSIMA BARBARA F.,HARRISON-TRAINOR MATTHEW
Abstract
AbstractThe
$\Omega $
numbers—the halting probabilities of universal prefix-free machines—are known to be exactly the Martin-Löf random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-Löf random left-c.e. real
$\alpha $
, a universal prefix-free machine U whose halting probability is
$\alpha $
. We also answer a question of Barmpalias and Lewis-Pye by showing that given a left-c.e. real
$\alpha $
, one cannot uniformly produce a left-c.e. real
$\beta $
such that
$\alpha - \beta $
is neither left-c.e. nor right-c.e.
Publisher
Cambridge University Press (CUP)
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