Some Algebraical and Logical Properties of Two-dimensional Arithmetical Sets Representable in Presburger’s System
Abstract
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.
References
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