Samuel Rathmanner and Marcus Hutter, "A Philosophical Treatise of Universal Induction"
in Entropy 2011, 13, 1076-1136. A very clear philosophical and mathematical analysis of Solomonoff's Theory of Inductive Inference.
An article about Algorithmic Probability is in the
Wikipedia .
For another detailed description of Algorithmic Probability, see "Algorithmic Probability"
by Marcus Hutter, Shane Legg, and Paul Vitanyi, in the Scholarpedia,(8):2572.
Peter Gacs and Paul Vitanyi, IEEE In Memoriam
gives an excellent discussion of Ray's work, with a detailed description of Solomonoff's General Theory of Inductive inference.
An article about the General Theory of Inductive Inference, and some of the variants by others is in the
Wikipedia ; parts of this article, however are very uneven
For a detailed description of Algorithmic Information Theory, see Algorithmic Information Theory, by Marcus Hutter,
in the Scholarpedia, 2(3):2519.