Computable paradoxical decompositions

TL;DR

This paper develops a computable framework for classical theorems in set theory and group theory, providing effective versions of Hall's Harem Theorem and Tarski's alternative theorem.

Contribution

It introduces computable analogues of key theorems, bridging classical results with computability theory for the first time.

Findings

Established a computable version of Hall's Harem Theorem.

Derived computable forms of Tarski's alternative theorem.

Demonstrated applications to computable set and group decompositions.

Abstract

We prove a computable version of Hall's Harem Theorem and apply it to computable versions of Tarski's alternative theorem.