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Evolutionary expansion theorem for universal kinematics
Grushka Yaroslav 1
1 Department of nonlinear analysis, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 01001, Ukraine
Keywords: еvolutionary expansion theorem for universal kinematics, set-theoretic relation, theory of relativity, the theory of kinematic changeable sets
Abstract
Analogs of the set-theoretic inclusion relation and the set-theoretic operation of union for universal kinematic sets are introduced. A theorem on evolutional extension for universal kinematic іs proved. The obtained results can be used for formulation of mathematical foundations of special relativity in the framework of the theory of kinematic changeable sets.
References

[1] Hilbert's Problems.  Collected under the editorship of P.S. Aleksandrov. - “Nauka”, Moscow. - 1969. - 240 p.

[2] A.D. Gladun. Hilbert's sixth problem.  // Potential. - 2006. - N 3.((http://potential.org.ru/Home/ ProblemGilbert).

[3]  Yu.I. Petunin, D.A. Klyushin. A structural approach to solving the 6th Hilbert problem. // Theory of Probability and Mathematical Statistics. - 2005. - N 71 . - P. 165-179.

[4] Adonai S. Sant'Anna. The definability of physical concepts. // Bol. Soc. Parana. Mat. (3s.). - 2005. - V 23 , N 1-2. - P. 163-175.

[5]  Newton C. A. da Costa, Adonai S. Sant'Anna. The mathematical role of time and space-time in classical physics. // Foundations of Physics Letters. - 2001. - V 14 , N 6. - P. 553-563.

[6] Grushka Y.I.. Primitive variable sets and their properties.” // Mathematical Bulletin of the National Technical School. - 2012 - Т 9 . - P. 52-80.

[7] Grushka Y.I. Variable sets and their properties. - 2012. - N 5 . - P. 12-18.

[8]  Ya.I. Grushka. Abstract concept of changeable set. - Preprint arXiv:1207.3751v1. - 2012.

[9] Grushka Y.I.. Visibility in changing sets.” // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 2012. - V. 9, N 2. - P. 122-145.

[10] Grushka Y.I.. Variable sets and their application for the construction of tachyon kinematics. - 2014. - V. 11, N 1. - P. 192-227.

[11] Grushka Y. I.. Basic variable sets and mathematical modeling of the evolution of systems.” // Ukr. math. zhurnal - 2013 - V. 65, N 9. - P. 1190-1210.

[12] Grushka Y.I. Criterion for the existence of a universal coordinate transformation in kinematic variable sets. - 2014. - V. 2, N 2-3. - P. 59-71.

[13] Grushka Y.I. Transformation of coordinates in kinematic variable sets. - 2015. - N 3. - P. 24-31.

[14] Grushka Y.I. Kinematic variable sets with a given universal coordinate transformation. - 2015. - V. 12, N 1. - P. 74-118.

[15]  Grushka Ya.I. Abstract Coordinate Transforms in Kinematic Changeable Sets and their Properties . - Preprint arXiv:1504.02685v2. - 2015.

[16]  Valentina Baccetti, Kyle Tate, Matt Visser. Inertial frames without the relativity principle . // Journal of High Energy Physics. - 2012. - V. 2012 , N 5.

[17]  Valentina Baccetti, Kyle Tate, and Matt Visser. Lorentz violating kinematics: Threshold theorems . // Journal of High Energy Physics. - 2012. - V. 2012, N 3.

[18]   Valentina Baccetti, Kyle Tate, and Matt Visser. Inertial frames without the relativity principle: breaking Lorentz symmetry . - Preprint: arXiv:1302.5989. - 2013.

[19] В. Pauli. Theory of relativity. - “Nauka”, Moscow. - 1991.  - 325 p.

[20] Grushka Y.I.. Evolutionary expansions and analogs of the union operation for basic variable sets. - 2014. - V. 11, N 2. - P. 66-99.

[21] Grushka Y.I. Evolutionary expansions of kinematic sets and universal kinematics. - 2015. - V. 12, N 2. - P. 139-204.

[22]  G. Birkhof.Theory of Lattices. - “Nauka”, Moscow. - 1984. - 567 p.

[23]  К. Kuratovsky, A. Mostovsky. Theory of sets. - Mir, Moscow. - 1970. - 416 p.

[24] Mendelsohn.Vvedeniya v matematicheskuyu logika . - “Nauka”, Moscow. - 1984. - 320 p.

Cite
ACS Style
Grushka, Y. Evolutionary expansion theorem for universal kinematics. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Grushka Y. Evolutionary expansion theorem for universal kinematics. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style
Yaroslav Grushka. 2016. "Evolutionary expansion theorem for universal kinematics". Bukovinian Mathematical Journal. 3 no. 3-4.
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