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Chang's Conjectures and Easton collapses

Monroe Eskew, Masahiro Shioya

Abstract

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

Chang's Conjectures and Easton collapses

Abstract

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
Paper Structure (7 sections, 14 theorems, 48 equations)

This paper contains 7 sections, 14 theorems, 48 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Easton collapse
  4. Iteration with product
  5. The main forcing
  6. Master conditions
  7. Proof of Theorem 1

Key Result

Theorem 1

Suppose $\kappa$ is 2-huge. Then there is a generic extension in which $\kappa=\omega_1$ and $(\omega_3,\omega_2,\omega_1)\twoheadrightarrow(\omega_2,\omega_1,\omega)$ holds.

Theorems & Definitions (24)

  • Theorem : Foreman
  • Theorem : Eskew
  • Theorem 1
  • Lemma 2
  • Lemma : Laver
  • Lemma 3
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 14 more