Nawrotzki's Algorithm for the Countable Splitting Lemma, Constructively

TL;DR

This paper presents a constructive algorithm based on Nawrotzki's approach for the countable splitting lemma, ensuring computability of each approximation step and the error, thus providing a practical method for the lemma.

Contribution

It introduces a new constructive algorithm that combines Nawrotzki's method with finite cuts to approximate solutions to the countable splitting lemma.

Findings

Algorithm converges to the solution

Each approximation and error is finitely computable

Provides a practical constructive proof

Abstract

We reprove the countable splitting lemma by adapting Nawrotzki's algorithm which produces a sequence that converges to a solution. Our algorithm combines Nawrotzki's approach with taking finite cuts. It is constructive in the sense that each term of the iteratively built approximating sequence as well as the error between the approximants and the solution is computable with finitely many algebraic operations.