Metric Baumgartner theorems and universality

Stefan Geschke, Menachem Kojman

Research output: Contribution to journalArticlepeer-review

Abstract

It is consistent with the axioms of set theory that for every metric space X which is isometric to some separable Banach space or to Urysohn's universal separable metric space U the following holds: (*)X There exists a nowhere meager subspace of X of cardinality N1 and any two nowhere meager subsets of X of cardinality N1 are almost isometric to each other. As a corollary, it is consistent that the Continuum Hypothesis fails and the following hold: (1) There exists an almost-isometry ultrahomogeneous and universal element in the class of separable metric spaces of size N1. (2) For every separable Banach space X there exists an almost-isometry conditionally ultrahomogeneous and universal element in the class of subspaces of X of size N1. (3) For every finite dimensional Banach space X, there is a unioue universal element up to almost-isometry in the class of subspaces of X of size N1

Original languageEnglish
Pages (from-to)215-226
Number of pages12
JournalMathematical Research Letters
Volume14
Issue number2-3
DOIs
StatePublished - 1 Jan 2007

Keywords

  • Almost-isometric embedding
  • Almost-isometry
  • Metric space
  • Oracle forcing
  • Universality
  • Urysohn's space

ASJC Scopus subject areas

  • General Mathematics

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