More infinity for a better finitism

Sam Sanders (1)

1 Department of Pure Mathematics and Computer Algebra

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes. Here, we discuss the inherent problems and limitations of the classical nonstandard framework and propose a much-needed refinement of , called , in the spirit of Karel Hrbacek's stratified set theory. We study the metamathematics of and its extensions. In particular, we consider several transfer principles, both classical and 'stratified', which turn out to be related. Finally, we show that the resulting theory allows for a truly general, elegant and elementary treatment of basic analysis.

Mots clés: 03H15; 26E35; Relative; Stratified; Nonstandard; Quantifier-free; Qnalysis; ERNA

Domaines: Logique [math.LO]

Sam Sanders. More infinity for a better finitism. Annals of Pure and Applied Logic, 2010, 161 (12), pp.1525. ⟨10.1016/j.apal.2010.06.003⟩. ⟨hal-00670733⟩