Premium
Imaginaries in Boolean algebras
Author(s) -
Wencel Roman
Publication year - 2012
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.201020082
Subject(s) - mathematics , combinatorics , equivalence relation , equivalence (formal languages) , algebra over a field , pure mathematics
Given an infinite Boolean algebra B , we find a natural class of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\varnothing$\end{document} ‐definable equivalence relations \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}_{B}$\end{document} such that every imaginary element from B eq is interdefinable with an element from a sort determined by some equivalence relation from \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}_{B}$\end{document} . It follows that B together with the family of sorts determined by \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {E}_{B}$\end{document} admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean algebras, obtained in 10.