On Interpretations of Bounded Arithmetic and Bounded Set Theory
Pettigrew, Richard
Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, p. 141-151 / Harvested from Project Euclid
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In "On interpretations of arithmetic and set theory," Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic. ¶ Theorem The first-order theories of Peano arithmetic and Zermelo-Fraenkel set theory with the axiom of infinity negated are bi-interpretable. ¶ In this note, I describe a theory of sets that is bi-interpretable with the theory of bounded arithmetic I Δ0 +exp . Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's interpretation of the arithmetic in the set theory. Instead, I am forced to produce a different interpretation.
Publié le : 2009-04-15
Classification:  I Delta 0 + exp,  finite set theory,  interpretations,  03C62 
@article{1242067707,
     author = {Pettigrew, Richard},
     title = {On Interpretations of Bounded Arithmetic and Bounded Set Theory},
     journal = {Notre Dame J. Formal Logic},
     volume = {50},
     number = {1},
     year = {2009},
     pages = { 141-151},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1242067707}
}

Pettigrew, Richard. On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp.  141-151. http://gdmltest.u-ga.fr/item/1242067707/