An unpublished theorem of Solovay, revisited

Linearization of partial quasi-orderings in the Solovay model revisited

We modify arguments in Vladimir Kanovei, Linearization of definable order relations, APAL, 102(1-2):69--100, 2000, to reprove a linearization theorem on real-ordinal definable partial quasi-orderings in the Solovay model.

Solovay 可归约性蕴含 S2a-可归约性

Solovay reducibility implies S2a-reducibility

本文证明在可计算逼近实数集合上，Solovay 可归约性蕴含 S2a-可归约性且常数相同，但反向蕴含不成立。

Random semicomputable reals revisited

The aim of this expository paper is to present a nice series of results, obtained in the papers of Chaitin (1976), Solovay (1975), Calude et al. (1998), Kucera and Slaman (2001). This joint effort led to a full characterization of lower semicomputable random reals, both as those that can be expressed as a "Chaitin Omega" and those that are maximal for the Solovay reducibility. The original proofs were somewhat involved; in this paper, we present these results in an elementary way, in particular requiring only basic knowledge of algorithmic randomness. We add also several simple observations re…