Introduction to E. Nelson’s internal set theory

Taras Kudryk

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2015)

  • Volume: 7, page 59-78
  • ISSN: 2080-9751

Abstract

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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.

How to cite

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Taras Kudryk. "Introduction to E. Nelson’s internal set theory." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 7 (2015): 59-78. <http://eudml.org/doc/296402>.

@article{TarasKudryk2015,
abstract = {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.},
author = {Taras Kudryk},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {Nonstandard Models in Analysis; Internal Set Theory},
language = {pol},
pages = {59-78},
title = {Introduction to E. Nelson’s internal set theory},
url = {http://eudml.org/doc/296402},
volume = {7},
year = {2015},
}

TY - JOUR
AU - Taras Kudryk
TI - Introduction to E. Nelson’s internal set theory
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2015
VL - 7
SP - 59
EP - 78
AB - 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.
LA - pol
KW - Nonstandard Models in Analysis; Internal Set Theory
UR - http://eudml.org/doc/296402
ER -

References

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  19. Lindstrøm, T.: 1988, An invitation to nonstandard analysis, w: N. J. Cultland (red.), Nonstandard analysis and its applications, Cambridge University Press, Cambridge, 1-105. 
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  21. Luxemburg, W. A. J., Robinson, A.: 1972, Contributions to Nonstandard Analysis, North-Holland Publishing Comp., Amsterdam, London. 
  22. Lyantse, W., Kudryk, T.: 1997, Introduction to Nonstandard Analysis, VNTL Publishes, Lviv. 
  23. Mendelson, E.: 1963, Introduction to Mathematical Logic, D. Van Nostrand Company, Inc., Princeton. 
  24. Nelson, E.: 1977, Internal Set Theory: A New Approach to Nonstandard Analysis, Bull. Amer. Math. Soc. 83(6), 1165-1198. 
  25. Nelson, E.: 1987, Radically Elementary Probability Theory, Princeton University Press, Princeton, New Jersey. 
  26. Nelson, E.: 1990, Ann. Pure Appl. Logic, The Syntax of Nonstandard Analysis. 
  27. Robert, A.: 1985, Analyse Non-standard, Presse Polythechnique Romandes, Lausanne. 
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  31. Stroyan, K. D., Luxemburg, W. A. J.: 1976, Introduction to the Theory of Infinitesimals, Academic Press, New York, London. 

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