On the Failure of BD-N and BD, and an Application to the Anti-Specker Property

TL;DR

This paper explores the failure of certain principles in constructive analysis using topological models, demonstrating that the anti-Specker property does not imply BD-N and analyzing the failure of BD and BD-N in various models.

Contribution

It introduces natural topological models for the failure of BD-N and BD, and clarifies how BD-N fails in known realizability models.

Findings

Closure of spaces with the anti-Specker property under product does not imply BD-N.

Provides topological models illustrating the failure of BD and BD-N.

Details how BD-N fails in specific realizability models.

Abstract

We give the natural topological model for the failure of BD-N, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-N. Also, the natural topological model for the failure of BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-N, it is brought out in detail how BD-N fails.