Abstract
It is known that IST (internal set theory) is a conservative extension of ZFC (Zermelo-Fraenkel set theory with the axiom of choice); see for example the appendix to [2] for a proof using ultrapowers and ultralimits. But these semantic constructions leave one wondering what actually makes the theory work—what are the inner mechanisms of Abraham Robinson’s new logic. Let us examine the question syntactically.
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References
Patrick Billingsley, Convergence of Probability Measures, second edition. Wiley & Sons, Inc., New York (1999).
Edward Nelson, “Internal set theory: A new approach to nonstandard analysis”, Bull. Amer. Math. Soc., 83 (1987) 1165–1198.
Edward Nelson, Radically Elementary Probability Theory, Annals of Mathematics Studies #117, Princeton University Press. Princeton, New Jersey (1987). http://www.math.princeton.edu/~nelson/books.html
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© 2007 Springer-Verlag Wien
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Nelson, E. (2007). The virtue of simplicity. In: van den Berg, I., Neves, V. (eds) The Strength of Nonstandard Analysis. Springer, Vienna. https://doi.org/10.1007/978-3-211-49905-4_2
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DOI: https://doi.org/10.1007/978-3-211-49905-4_2
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-49904-7
Online ISBN: 978-3-211-49905-4
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