Forcing in nonstandard analysis. (English) Zbl 0812.03041
The results and methods in this paper could lead to a significant improvement within the discipline of nonstandard analysis. A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. Much of this paper is taken up with such a construction and showing how this construction’s properties compare with those of the usual nonstandard universe. With this new framework at hand, the author is able to give an example of an \(\aleph_ 1\)-saturated Boolean ultrapower of the real number field that is not Scott complete. Other applications are to a generic extension of the hyperreal numbers, a hull completeness theorem and Loeb measure.
Reviewer: R.A.Herrmann (Annapolis)
MSC:
| 03H05 | Nonstandard models in mathematics |
| 03E40 | Other aspects of forcing and Boolean-valued models |
Keywords:
nonstandard analysis; nonstandard universe; superstructure; Boolean- valued model of set theory; Boolean ultrapower; Scott complete; generic extension of the hyperreal numbers; hull completeness theorem; Loeb measureReferences:
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