You're confusing the statement "The Kolgomorov complexity of all strings is zero" with "For every string there exists a definition of Kolmogorov complexity i

You're confusing the statement "The Kolgomorov complexity of all strings is zero" with "For every string there exists a definition of Kolmogorov complexity in which that string has complexity 0" The first (which you claim as a Theorem) presumes an already fixed definition of complexity, and is therefore false, while the second is what you proof, and which is not interesting. Here's how I would fix the definition of Kolmogorov Complexity: https://en.wikipedia.org/wiki/Binary_lambda_calculus https://en.wikipedia.org/wiki/Binary_lambda_calculus