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On ultrafilters in ZF models and indecomposable ultrafilters

Eilon Bilinsky, Moti Gitik

Abstract

We use indecomposable ultrafilters to answer some questions of Hayut, Karagila paper "Spectra of uniformity". It is shown that the bound on the strength by T. Usuba "A note on uniform ultrafilters in choiceless context" is optimal.

On ultrafilters in ZF models and indecomposable ultrafilters

Abstract

We use indecomposable ultrafilters to answer some questions of Hayut, Karagila paper "Spectra of uniformity". It is shown that the bound on the strength by T. Usuba "A note on uniform ultrafilters in choiceless context" is optimal.
Paper Structure (3 sections, 4 theorems, 5 equations)

This paper contains 3 sections, 4 theorems, 5 equations.

Table of Contents

  1. On indecomposable ultrafilters
  2. On existence of indecomposable ultrafilters on non-measurable cardinals
  3. Applications to ZF models

Key Result

Theorem 1.6

Let $\delta$ and $\kappa$ be cardinals with $2^\delta<\kappa$. Suppose that $U$ is a $(\delta,\kappa)-$indecomposable ultrafilter over a set $I$. Then $j_U = j_W^{M_D}\circ j_D$ where $D$ is an ultrafilter over a cardinal less than $\delta$ and $W$ is an $M_D-\kappa-$complete $M_D-$ultrafilter over

Theorems & Definitions (8)

  • Definition 1.1
  • Theorem 1.6
  • Theorem 1.7
  • Claim 1
  • Claim 2
  • Claim 3
  • Theorem 1.8
  • Theorem 3.1