Abstract
AbstractGiven an infinite Boolean algebraB, 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 fromBeqis 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 thatBtogether 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 in10.
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