Decomposability of ℝ and dense negative subsets of ℝ in constructive reverse mathematics
Abstract We show that over BISH, the decomposability of $\mathbb{R}$ is equivalent to WLPO. Let $D\subseteq \mathbb{R} \setminus \{0\}$ be a dense negative subset of $\mathbb{R}$. It is shown that over BISH, the decomposability of $D$ is equivalent to $\textbf{MP}^{\lor }$.
Authors
- Mohammad Ardeshir
- Mohammad Tahmasbizadeh
Institutions
- Sharif University of Technology (IR)
Publication Details
- Journal
- Logic Journal of IGPL
- Published
- 2025-11-26
- DOI
- https://doi.org/10.1093/jigpal/jzaf092
- Primary Topic
- Computability, Logic, AI Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00