Voir la notice de l'article provenant de la source Math-Net.Ru
Keywords: algorithms on physical objects, general system theory, general formal technology, object properties, object functionalities, axiomatic of metaphysics, evolutionary systems.
S. M. Krylov. Prospects of metamathematical structures in science. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 131 (2013) no. 2, pp. 101-110. http://geodesic.mathdoc.fr/item/VSGTU_2013_131_2_a11/
@article{VSGTU_2013_131_2_a11,
author = {S. M. Krylov},
title = {Prospects of metamathematical structures in science},
journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
pages = {101--110},
year = {2013},
volume = {131},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_131_2_a11/}
}
TY - JOUR AU - S. M. Krylov TI - Prospects of metamathematical structures in science JO - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences PY - 2013 SP - 101 EP - 110 VL - 131 IS - 2 UR - http://geodesic.mathdoc.fr/item/VSGTU_2013_131_2_a11/ LA - ru ID - VSGTU_2013_131_2_a11 ER -
[1] S. C. Kleene, Introduction to metamathematics, Bibliotheca Mathematica, 1, North-Holland Publishing Co., Amsterdam, 1952, x+550 pp. ; S. K. Klini, Vvedenie v metamatematiku, Knizhnyi dom «Librakom», M., 2009, 528 pp. | MR | Zbl
[2] W. Fontana, L. W. Buss, “The barrier of objects: From dynamical systems to bounded organizations”, Boundaries and Barriers, ed. J. Casti and A. Karlqvist, Addison-Wesley, Reading MA, 1996, 56–116
[3] S. M. Krylov, “General formal technology and algorithmic theory of objects calculus”, Computer Technologies in Science, Practice, and Education, Samara State Technical Univ., Samara, 2012, 27–30
[4] S. M. Krylov, “Mathematical foundations of metaphysics”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(26) (2012), 233–242 | DOI
[5] S. M. Krylov, Ontology of Meta-Science. Axioms, Technology, Algorithms, Evolution (in Russian), LAP LAMBERT Academic Publ., Saarbrücken, 2012, 408 pp.
[6] A. I. Malcev, Algebraic Systems, Springer-Verlag, Berlin, 1973, xii+317 pp. | MR | MR | Zbl
[7] Aristotle, Metaphysics. Translations. Comments. interpretation, ed. entry by S. I.Eremeev, Aleteyya, St. Petersburg, 2002, 832 pp.
[8] A. A. Lovelace, “Notes by the Translator”, Faster than Thought. A Symposium on Digital Computing Machines, ed. B. V. Bowden, London, 1957, 362–408
[9] Algorithms in Modern Mathematics and Its Applications, SO AN SSSR, Novosibirsk, 1982, 364 pp.
[10] B. Jones, “General System Theory and Algorithm Theory”, Int. J. Gen. Syst., 9:3 (1983), 157–160 | DOI | Zbl
[11] S. M. Krylov, “Models of universal discrete-analog machines based on Turing machine”, Elektronnoye modelirovaniye, 1982, no. 3, 6–10 | MR
[12] J. R. Shoenfield, Degrees of unsolvability, North-Holland Mathematics Studies, 2, Nort-Holland Publishing Comp., Amsterdam, London; American Elsevier Publishing Comp., New York, 1971, 111 pp. ; Dzh. Shenfild, Stepeni nerazreshimosti, Nauka, M., 1977, 192 pp. | MR | Zbl | MR
[13] G. J. Chaitin, Proving Darwin. Making Biology Mathematical, Pantheon Books, New York, 2012, 124 pp.
[14] S. M. Krylov, “The proof of action boundedness for Turing–Church thesis on objects with physical properties”, Vestn. Orenburg. Gos. Univ., 2003, no. 3, 102–105
[15] J. B. Copeland, “Hypercomputation”, Minds Mach., 12:4 (2002), 461–502 | DOI | Zbl
[16] S. M. Krylov, V. N. Tolchev, “Multifunction remote laboratories to carry out real laboratory work and experiments”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Tekhn. Nauki, 2011, no. 1(29), 85–91
[17] S. M. Krylov, “Universal Programmable Completely Automated Factories-on-a-Chip”, Proceedings of the 9$^{th}$ International Conference on the Commercialization of Micro and Nano Systems COMS2004. (Aug. 29 – Sept. 2, 2004), Edmonton, Alberta, Canada, MANCEF, Washington, 2004, 269–273
[18] G. J. Chaitin, “A Century of Controversy over the Foundations of Mathematics”, Finite versus Infinite, ed. C. Calude and G. Paun, Springer-Verlag, London, 2000, 75–100 | DOI | MR
[19] S. M. Krylov, “The relationship between entropy, structural and functional description of objects and systems”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2003, no. 19, 156–160 | DOI
[20] S. M. Krylov, “Formally-technological models in the general systems theory”, Izv. Samarsk. Nauchn. Tsentra RAN, 5:1 (2003), 83–90 | MR
[21] S. M. Krylov, “System analysis of heterogeneous weakly-structured automata I. Basic definitions and behavior”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Tekhn. Nauki, 2012, no. 1(33), 17–23
[22] S. M. Krylov, E. N. Grebenschikov, “Ontology of heterogenious electronics systems design”, Ontologiya proyektirovaniya, 2012, no. 1, 65–72
[23] J. von Neumann, Theory of Self-Reproducing Automata, ed. A. W. Burks, University of Illinois Press, Urbana, London, 1966, xix+388 pp.; Dzh. fon Neiman, Teoriya samovosproizvodyaschikhsya avtomatov, Mir, M., 1971, 284 pp.
[24] S. W. Hawking, The Theory of Everything: The Origin and Fate of the Universe, New Millennium Press, New York, 2002, 167 pp.