Principles Weaker than BD-N

TL;DR

This paper investigates the relative strength of the principle BD-N in constructive analysis, showing that several principles implied by BD-N are strictly weaker but not provable in basic set theory.

Contribution

It demonstrates that certain principles implied by BD-N are strictly weaker yet not provable in set theory, clarifying their position in constructive analysis.

Findings

Closure of anti-Specker spaces under product is weaker than BD-N

Riemann Permutation Theorem is weaker than BD-N

All partially Cauchy sequences are weaker than BD-N

Abstract

BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set theory alone under constructive logic.