Kanoveĭ, V. G.; Lyubetskiĭ, V. A. Problems of set-theoretic non-standard analysis. (English. Russian original) Zbl 1226.03067 Russ. Math. Surv. 62, No. 1, 45-111 (2007); translation from Usp. Mat. Nauk 62, No. 1, 51-122 (2007). Summary: The main results in the area of set-theoretic nonstandard analysis (nonstandard set and class theories) obtained over the last few years are presented. It is demonstrated how a universe of a comparably simple theory (beginning with the usual Zermelo-Fraenkel set theory ZFC) can be extended to a universe of a more complicated nonstandard set or class theory. The last section develops the foundations of Boolean-valued analysis as a part of set-theoretic nonstandard analysis. Cited in 4 Documents MSC: 03H05 Nonstandard models in mathematics 03E40 Other aspects of forcing and Boolean-valued models 03E70 Nonclassical and second-order set theories 46S20 Nonstandard functional analysis 54J05 Nonstandard topology Keywords:nonstandard set theory; nonstandard class theory; Boolean-valued analysis PDFBibTeX XMLCite \textit{V. G. Kanoveĭ} and \textit{V. A. Lyubetskiĭ}, Russ. Math. Surv. 62, No. 1, 45--111 (2007; Zbl 1226.03067); translation from Usp. Mat. Nauk 62, No. 1, 51--122 (2007) Full Text: DOI