Lattices in generative classes

Yiannis Kiouvrekis, Petros Stefaneas, Sergey Vladimirovich Sudoplatov

Research output: Contribution to journalArticlepeer-review

Abstract

We define and study lattices in generative classes associated with generic structures. It is shown that these lattices can be non-distributive and, moreover, arbitrary enough. Heights and wights of the lattices are described. A model-theoretic criterion for the linear ordering is proved and these linear orders are described. Boolean algebras generated by the considered lattices are also described.

Original languageEnglish
Pages (from-to)1752-1761
Number of pages10
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Boolean algebra
  • Generative class
  • Generic structure
  • Lattice
  • Linear order

OECD FOS+WOS

  • 1.01 MATHEMATICS

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