Nonstandard models of arithmetic as an alternative basis for continuum considerations. (English) Zbl 0531.03045

Čuda, Karel

Commentat. Math. Univ. Carol. 24, 415-430 (1983).

Summary: From the point of view of 1) nonstandard models of arithmetic: A special type of strong cuts in the sense of Kirby and Paris are considered. It is proved that the pair of such a cut and the corresponding ground model may serve as a basis for an alternative construction of real numbers. Some other set theoretical properties are proved. 2) Nonstandard analysis: Using nonstandard methods a model for real numbers is constructed in a theory much weaker than Zermelo-Fraenkel set theory. 3) Alternative set theory: Considerations in a fragment of AST are made and a contribution to the shiftings of horizon problem is given.

MSC:

03H15	Nonstandard models of arithmetic
03E70	Nonclassical and second-order set theories
03H05	Nonstandard models in mathematics

Keywords:

nonstandard model of Peano arithmetic; alternative set theory; strong cut; indiscernibility relation; prolongation