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Littlewood's principles in reverse real analysis

Rafael Reno S. Cantuba

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.

Littlewood's principles in reverse real analysis

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.
Paper Structure (3 sections, 1 theorem, 19 equations)

This paper contains 3 sections, 1 theorem, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Equivalence of Littlewood's Principles to the Cut Axiom

Key Result

Theorem 3.1

For an arbitrary ordered field $\mathbb{F}$, each of the statements is equivalent to (CA).

Theorems & Definitions (2)

  • Theorem 3.1
  • proof