On products of elementarily indivisible structures

Nadav Meir

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We say a structure M in a first-order language L is indivisible if for every coloring of its universe in two colors, there is a monochromatic substructure M′ ⊆ M such that M ≅ M. Additionally, we say thatMis symmetrically indivisible if M′ can be chosen to be symmetrically embedded in M (that is, every automorphism of M′ can be extended to an automorphism of M). Similarly, we say that M is elementarily indivisible if M′ can be chosen to be an elementary substructure. We define new products of structures in a relational language. We use these products to give recipes for construction of elementarily indivisible structures which are not transitive and elementarily indivisible structures which are not symmetrically indivisible, answering two questions presented by A. Hasson, M. Kojman, and A. Onshuus.

Original languageEnglish
Pages (from-to)951-971
Number of pages21
JournalJournal of Symbolic Logic
Issue number3
StatePublished - 1 Sep 2016


  • Coloring
  • Elementary indivisibility
  • Indivisibility
  • Quantifier elimination

ASJC Scopus subject areas

  • Philosophy
  • Logic


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