Chaitin's incompleteness theorem states that sufficiently rich formal systems cannot prove lower bounds on Kolmogorov complexity. In this paper we extend this theorem by showing theories that prove the Kolmogorov complexity of a large (but finite) number of strings are inaccessible. This is done by first showing such theories have large information with the halting sequence. Then, by applying the independence postulate, such theories are shown to be inaccessible in the physical world.

翻译：柴廷不完全性定理指出，足够丰富的形式系统无法证明柯尔莫哥洛夫复杂度的下界。在本文中，我们通过证明那些能确定大量（但有限）字符串的柯尔莫哥洛夫复杂度的理论是无法触及的，来扩展这一定理。首先，我们证明此类理论包含关于停机序列的大量信息；然后，应用独立性假设，进一步表明这些理论在物理世界中是无法实现的。