# Littlewood's principles in reverse real analysis

## TL;DR

This paper explores the relationship between Littlewood's principles and the completeness axiom within ordered fields, showing their equivalence when formulated as axioms in reverse real analysis.

## Contribution

It establishes that local forms of Littlewood's principles are equivalent to the completeness axiom in the context of ordered fields.

## Key findings

- Local Littlewood's principles are equivalent to the completeness axiom.
- Axiomatization of Littlewood's principles in ordered fields.
- Equivalence holds in reverse real analysis context.

## Abstract

If local forms of Littlewood's three principles are stated as axioms for an ordered field, then each principle is equivalent to the completeness axiom.