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A unique $Q$-point and infinitely many near-coherence classes of ultrafilters

Lorenz Halbeisen, Silvan Horvath, Saharon Shelah

Abstract

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-$ω_2$ countable support iteration of restricted Mathias forcing over a ground model satisfying $\textsf{CH}$, there is a unique $Q$-point up to isomorphism. In particular, it is consistent that there is only one $Q$-point while there are $2^{\mathfrak{c}}$-many near-coherence classes of ultrafilters.

A unique $Q$-point and infinitely many near-coherence classes of ultrafilters

Abstract

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length- countable support iteration of restricted Mathias forcing over a ground model satisfying , there is a unique -point up to isomorphism. In particular, it is consistent that there is only one -point while there are -many near-coherence classes of ultrafilters.

Paper Structure

This paper contains 6 sections, 23 equations.

Table of Contents

  1. Introduction
  2. Note added in proof:
  3. Definitions and Preliminaries
  4. Result
  5. Case I.
  6. Case II.

Theorems & Definitions (7)

  • proof
  • proof
  • proof
  • proof
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  • proof
  • proof