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Todorcevic's Problem on Rado's Conjecture

Monroe Eskew, Rahman Mohammadpour

Abstract

In his Mostowski lecture in Wrocław in 2024, Stevo Todorčević asked whether it is consistent that Rado's Conjecture holds at two successive cardinals. We show that it is consistent that Rado's Conjecture holds at all regular cardinals.

Todorcevic's Problem on Rado's Conjecture

Abstract

In his Mostowski lecture in Wrocław in 2024, Stevo Todorčević asked whether it is consistent that Rado's Conjecture holds at two successive cardinals. We show that it is consistent that Rado's Conjecture holds at all regular cardinals.
Paper Structure (4 sections, 4 theorems, 2 equations)

This paper contains 4 sections, 4 theorems, 2 equations.

Table of Contents

  1. Introduction
  2. Basics
  3. Rado's Conjecture and its variants
  4. Global Rado's Conjecture

Key Result

Theorem 1.1

Let $\kappa$ be a cardinal below a supercompact cardinal $\lambda$. Then $\mathrm{RC}(\kappa^+)$ holds in $V^{\mathrm{Col}(\kappa^+,{<}\lambda)}$.

Theorems & Definitions (10)

  • Definition 1: Todorčević Tod85articlePart
  • Definition 2: Generalized Rado's Conjecture Tod83articleOn-a
  • Theorem 1.1: Todorčević Tod83articleOn-a
  • Lemma 1: Todorčević Tod83articleOn-a
  • proof
  • Definition 3
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof