Infinite lexicographic products

Nadav Meir

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define dense substructures in infinite products and show that any countable product of countable transitive homogeneous structures has a unique countable dense substructure, up to isomorphism. Furthermore, this dense substructure is transitive, homogeneous and elementarily embeds into the product. This result is then utilized to construct a rigid elementarily indivisible structure.

Original languageEnglish
Article number102991
JournalAnnals of Pure and Applied Logic
Volume173
Issue number1
DOIs
StatePublished - 1 Jan 2022

Keywords

  • Elementary indivisibility
  • Homogeneous structures
  • Indivisibility
  • Infinitary logic
  • Lexicographic product
  • Quantifier elimination

ASJC Scopus subject areas

  • Logic

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