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Bqo for Borel functions between Polish zero-dimensional spaces

Determine whether continuous reducibility is a better-quasi-order on the class of Borel functions between Polish zero-dimensional spaces.

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Background

The main results establish bqo for continuous reducibility on continuous functions under zero-dimensionality and separability assumptions. This conjecture strengthens the setting to Borel (not necessarily continuous) functions between Polish zero-dimensional spaces, seeking to extend bqo beyond continuity.

References

Here is the very first conjecture one can think of after MainTheorem1.

Conjecture Continuous reducibility is a bqo on Borel functions between Polish zero-dimensional spaces.

— A well-quasi-order for continuous functions (2410.13150 - Carroy et al., 17 Oct 2024) in Section 7.3 (DirectionPolish)