Universal structures

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We deal with the existence of universal members in a given cardinality for several classes. First, we deal with classes of abelian groups, specifically with the existence of universal members in cardinalities which are strong limit singular of countable cofinality or A D A o. We use versions of being reduced-replacing Q by a subring (defined by a sequence t)- and get quite accurate results for the existence of universals in a cardinal, for embeddings and for pure embeddings. Second, we deal with (variants of) the oak property (from a work of Džamonja and the author), a property of complete first-order theories sufficient for the nonexistence of universal models under suitable cardinal assumptions. Third, we prove that the oak property holds for the class of groups (naturally interpreted, so for quantifier-free formulas) and deals more with the existence of universals.

Original languageEnglish
Pages (from-to)159-177
Number of pages19
JournalNotre Dame Journal of Formal Logic
Volume58
Issue number2
DOIs
StatePublished - 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 by University of Notre Dame.

Keywords

  • Abelian groups
  • Classification theory
  • Groups
  • Model theory
  • The oak property
  • Universal models

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