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ω ‐categorical weakly o‐minimal expansions of Boolean lattices
Author(s) -
Leonesi Stefano,
Toffalori Carlo
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310042
Subject(s) - categorical variable , mathematics , lattice (music) , sequence (biology) , boolean algebras canonically defined , two element boolean algebra , stone's representation theorem for boolean algebras , boolean algebra , discrete mathematics , combinatorics , pure mathematics , algebra over a field , algebra representation , statistics , physics , biology , acoustics , genetics
We study ω ‐categorical weakly o‐minimal expansions of Boolean lattices. We show that a structure = ( A ,≤, ℐ) expanding a Boolean lattice ( A ,≤) by a finite sequence I of ideals of A closed under the usual Heyting algebra operations is weakly o‐minimal if and only if it is ω ‐categorical, and hence if and only if A/I has only finitely many atoms for every I ∈ ℐ. We propose other related examples of weakly o‐minimal ω ‐categorical models in this framework, and we examine the internal structure of these models.