Geodesic
On decidability of finite subsets’ theory for dense linear order
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2023), pp. 24-35
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We consider atomless boolean algebras, and study algebraic structures where the universe consists of finite subsets of such an algebra. On these structures, we define the new relation between finite subsets: we say that one set is less than another one iff all elements of the first set are less than all elements of the second one. We show that the theory of constructed structure is reducible to the theory of original boolean algebra. Hence, the theory of constructed structure is decidable.
Keywords: atomless boolean algebras, theory, finite subset, decidability. 
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N. V. Avkhimovich; S. M. Dudakov. On decidability of finite subsets’ theory for dense linear order. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2023), pp. 24-35. http://geodesic.mathdoc.fr/item/VTPMK_2023_1_a1/

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