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

Authors

  • Seda N. Manukian Institute for Informatics and Automation Problems of NAS RA

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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D. Hilbert und P. Bernays. Grundlagen der Mathematik. Band I. Zweite Auflage, Berlin-Heidelberg- New York, Springer Verlag, 1968.

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S. N. Manukian, “A Classification of Arithmetical Sets Expressible in Presburger's System”, Proceedings of the International Conference «Computer Science and Information Technologies», CSIT- 05, Yerevan, Armenia, pp. 161-162, 2005.

S. N. Manukian, “On the Representation of Recursively Enumerable Sets in Weak Arithmetic. Mathematical Problems of Computer Science, vol. 27, pp. 90-110, 2006.

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Published

2021-12-10

How to Cite

Manukian, S. N. . (2021). Some Algebraical and Logical Properties of Two-dimensional Arithmetical Sets Representable in Presburger’s System. Mathematical Problems of Computer Science, 37, 64–74. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/254