Gacs-Kucera theorem

Gacs - Kucera Theorem [2,3,5], tightened by Barmpalias, Lewis-Pye [1], w.t.t.-reduces each infinite sequence to a Kolmogorov - Martin-Lof random one and is broadly used in various Math and CS areas. Its early proofs are somewhat cumbersome, but using some general concepts yields significant simplification illustrated below. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The Gacs-Kucera theorem is an important tool in mathematics and computer science, which can reduce infinite sequences to random sequences. The early proofs of this theorem were somewhat cumbersome, but the use of general concepts can significantly simplify the proof process.