Scholarlink

<p>In the first part of this paper we produce models where <i>κ</i> is certain very large cardinal and every ground model <i>κ</i>-complete ultrafilter extends to a non-Galvin one. In the opposite direction, we also produce such models but this time every ground model <i>κ</i>-complete ultrafilter extends to a <i>P</i>-point ultrafilter, hence to a Galvin one. Finally, we apply Galvin’s property to obtain consistently new instances of the classical problem in partition calculus λ → (λ, <i>ω</i> + 1)<sup>2</sup> both in ZFC and ZF.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Galvin’s property at large cardinals and an application to partition calculus

  • 期刊论文

  • 发表日期：

    2025年4月3日

查看全文
  • Tom Benhamou,
  • Shimon Garti,
  • Alejandro Poveda

摘要

In the first part of this paper we produce models where κ is certain very large cardinal and every ground model κ-complete ultrafilter extends to a non-Galvin one. In the opposite direction, we also produce such models but this time every ground model κ-complete ultrafilter extends to a P-point ultrafilter, hence to a Galvin one. Finally, we apply Galvin’s property to obtain consistently new instances of the classical problem in partition calculus λ → (λ, ω + 1)2 both in ZFC and ZF.