An omega-power of a context-free language which is Borel above Delta^0_omega

TL;DR

This paper constructs a Borel set of infinite rank using erasers-like operations on words, demonstrating an omega-power of a context-free language that exceeds Delta^0_omega in the Borel hierarchy.

Contribution

It introduces a novel construction of a Borel set of infinite rank as an omega-power of a context-free language using erasers-like operations.

Findings

First example of an omega-power of a context-free language that is Borel of infinite rank

Uses erasers-like operations to achieve complex Borel hierarchy placement

Demonstrates the set is above Delta^0_omega in the Borel hierarchy

Abstract

We use erasers-like basic operations on words to construct a set that is both Borel and above Delta^0_omega, built as a set V^\omega where V is a language of finite words accepted by a pushdown automaton. In particular, this gives a first example of an omega-power of a context free language which is a Borel set of infinite rank.