Imaginaries in Boolean algebras |
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Authors: | Roman Wencel |
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Institution: | Instytut Matematyczny Uniwersytetu Wroc?awskiego, Pl. Grunwaldzki 2/4, 50‐384 Wroc?aw, Poland |
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Abstract: | Given an infinite Boolean algebra B, we find a natural class of $\varnothing$‐definable equivalence relations $\mathcal {E}_{B}$ such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from $\mathcal {E}_{B}$. It follows that B together with the family of sorts determined by $\mathcal {E}_{B}$ 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 . |
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Keywords: | Boolean algebra elimination of imaginaries msc (2010) 03C60 03G05 |
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