Autostability relative to strong constructivizations of Boolean algebras with distinguished ideals
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We study Boolean algebras with distinguished ideals (I-algebras). We proved that a local I-algebra is autostable relative to strong constructivizations if and only if it is a direct product of finitely many prime models. We describe complete formulas of elementary theories of local Boolean algebras with distinguished ideals and a finite tuple of distinguished constants. We show that countably categorical I-algebras, finitely axiomatizable I-algebras, superatomic Boolean algebras with one distinguished ideal, and Boolean algebras are autostable relative to strong constructivizations if and only if they are products of finitely many prime models.
KeywordsBoolean algebra Boolean algebra with distinguished ideals I-algebra autostability strong constructivizability autostability relative to strong constructivizations prime model
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