Di Nasso, Mauro Linearly stratified models for the foundations of nonstandard mathematics. (English) Zbl 0891.03035 Math. Log. Q. 44, No. 1, 138-142 (1998). Assuming the existence of an inaccessible cardinal, the author shows that there exist models of set theory that are transitive full and possess a linearly valued rank function. It is then shown that such models provide a global framework for nonstandard mathematics. Reviewer: W.A.J.Luxemburg (Pasadena) MSC: 03H99 Nonstandard models 03C20 Ultraproducts and related constructions 03C62 Models of arithmetic and set theory 03E55 Large cardinals Keywords:inaccessible cardinal; models of set theory; transitive full; linearly valued rank function; global framework for nonstandard mathematics PDFBibTeX XMLCite \textit{M. Di Nasso}, Math. Log. Q. 44, No. 1, 138--142 (1998; Zbl 0891.03035) Full Text: DOI References: [1] Boffa, Bull. Soc. Math. Belg. 21 pp 16– (1969) [2] Ballard, J. Symbolic Logic 57 pp 741– (1992) [3] and , Model Theory. 3rd ed. North-Holland Publ. Comp., Amsterdam 1990. [4] Forti, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (IV) 10 pp 493– (1983) [5] Set Theory. Academic Press, New York 1978. [6] A new variant of nonstandard analysis. In: Victoria Symposium on Nonstandard Analysis ( and , eds.), Lecture Notes in Mathematics 369, Springer-Verlag, Berlin-Heidelberg-New York 1974, pp. 313–339. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.