Some Algebraical and Logical Properties of Two-dimensional Arithmetical Sets Representable in Presburger’s System - Manukian, Seda N. (Mathematical Problems of Computer Science, 2021)
A classification (0)  (1)  (2)  ... H H H of arithmetical sets representable in M.Presburger’s system ([1]-[4]) and a classification (0)  (1)  (2)  ... H H H of twodimensional sets of the same kind are considered. It is proved that these classifications are strictly monotone and complete. The operations ,,  ,  , 1 on twodimensional arithmetical sets ([5]-[7]) and the algebras Θ0 and Θ1 based on these operations ([5]-[7]) are considered. The relations of these operations and algebras to the mentioned classifications are investigated.