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2015 | 7 | 59-78
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Introduction to E. Nelson’s internal set theory

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An axiomatic approach to Non-standard Analysis by E. Nelsonis presented in a simplified form. The main aim of the article is strictly thepopularization of NSA, and not its foundations. No special preparation inmathematical logic is required from the reader but it is assumed that he(she) is familiar with elementary calculus and linear algebra.
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Bibliografia
  • Albeverio, S., Fenstad, J., Høegh-Krohn, R., Lindstrøm, T.: 1986, Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, Orlando.
  • Ballard, D.: 1994, Foundational Aspects of ”Non”standard Mathematics, Contemporary Mathematics 176. AMS.
  • Conway, J.: 1976, On Numbers and Games, Academic Press, London, New York, San Francisco.
  • Cutland, N. J.: 1983, Nonstandard Measure Theory and its Applications, Bull. London Math. Soc. 14(6), 529-589.
  • Cutland, N. J.: 1988, Nonstandard Analysis and its Applications, Cambridge University Press.
  • Davis, M.: 1977, Applied Nonstandard Analysis, Wiley, New York.
  • Diener, F.: 1983, Cours d’analyse nonstandard, Offices des Publ. Univ., Alger.
  • Diener, F., Reeb, G.: 1989, Analyse Nonstandard, Hermann, Ed. Sc. Arts.
  • Diener, F., Stroyan, K. D.: 1988, Syntactical Methods in Infinitesimal Analysis, w: N. J. Cutland (red.), Nonstandard Analysis and its Applications, Cambridge University Press, 258-281.
  • Goldblatt, R.: 1998, Lectures on the Hyperreals, Springer, New York.
  • Gordon, E. I., Kusraev, A. G., Kutateladze, S. S.: 2002, Infinitesimal Analysis, Kluwer Academic Publishers, Dordrecht.
  • Hrba˘cek, K.: 1979, Nonstandard Set Theory, Amer. Math. Monthly 86(8), 659-677.
  • Hrba˘cek, K.: 1987, Axiomatic Foundations for Nonstandard Analysis, Fund. Math. 98(1), 1-24.
  • Hrba˘cek, K., Lessman, O., O’Donovan, R.: 2015, Analysis with Ultrasmall numbers, CRC Press Taylor & Francis Group.
  • Hurd, A. E., Loeb, P. A.: 1985, Introduction to Nonstandard Real Analysis, Academic Press, New York.
  • Kanovei, V., Reeken, M.: 2004, Nonstandard Analysis, Axiomatically, Springer.
  • Kawai, T.: 1981, Axiom System of Nonstandard Set Theory, Logic symposia, Hakone 1979, 1980, Springer, 57-65.
  • Keisler, H. J.: 1976, Foundations of Infinitesimal Calculus, Prindle, Weber and Schmidt, Boston, Massachusets.
  • Lindstrøm, T.: 1988, An invitation to nonstandard analysis, w: N. J. Cultland (red.), Nonstandard analysis and its applications, Cambridge University Press, Cambridge, 1-105.
  • Lutz, R., Goze, M.: 1981, Nonstandard Analysis: a Practical Guide with Applications, Vol. 881, Lect. Notes in Math.
  • Luxemburg, W. A. J., Robinson, A.: 1972, Contributions to Nonstandard Analysis, North-Holland Publishing Comp., Amsterdam, London.
  • Lyantse, W., Kudryk, T.: 1997, Introduction to Nonstandard Analysis, VNTL Publishes, Lviv.
  • Mendelson, E.: 1963, Introduction to Mathematical Logic, D. Van Nostrand Company, Inc., Princeton.
  • Nelson, E.: 1977, Internal Set Theory: A New Approach to Nonstandard Analysis, Bull. Amer. Math. Soc. 83(6), 1165-1198.
  • Nelson, E.: 1987, Radically Elementary Probability Theory, Princeton University Press, Princeton, New Jersey.
  • Nelson, E.: 1990, Ann. Pure Appl. Logic, The Syntax of Nonstandard Analysis.
  • Robert, A.: 1985, Analyse Non-standard, Presse Polythechnique Romandes, Lausanne.
  • Robert, A.: 1988, Nonstandard Analysis, Wiley, New York and Chichester.
  • Robinson, A.: 1966, Non-standard Analysis, North-Holland Publishing Company, Amsterdam.
  • Shoenfield, J.: 1967, Mathematical Logic, Wesley.
  • Stroyan, K. D., Luxemburg, W. A. J.: 1976, Introduction to the Theory of Infinitesimals, Academic Press, New York, London.
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Bibliografia
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bwmeta1.element.ojs-issn-2450-341X-year-2015-volume-7-article-3631
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