The Strength of Nonstandard Methods in Arithmetic
Henson, C. Ward ; Kaufmann, Matt ; Keisler, H. Jerome
J. Symbolic Logic, Tome 49 (1984) no. 1, p. 1039-1058 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We consider extensions of Peano arithmetic suitable for doing some of nonstandard analysis, in which there is a predicate $N(x)$ for an elementary initial segment, along with axiom schemes approximating $\omega_1$-saturation. We prove that such systems have the same proof-theoretic strength as their natural analogues in second order arithmetic. We close by presenting an even stronger extension of Peano arithmetic, which is equivalent to ZF for arithmetic statements.
Publié le : 1984-12-14
Classification:  
@article{1183741687,
     author = {Henson, C. Ward and Kaufmann, Matt and Keisler, H. Jerome},
     title = {The Strength of Nonstandard Methods in Arithmetic},
     journal = {J. Symbolic Logic},
     volume = {49},
     number = {1},
     year = {1984},
     pages = { 1039-1058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183741687}
}

Henson, C. Ward; Kaufmann, Matt; Keisler, H. Jerome. The Strength of Nonstandard Methods in Arithmetic. J. Symbolic Logic, Tome 49 (1984) no. 1, pp.  1039-1058. http://gdmltest.u-ga.fr/item/1183741687/