Arithmetical independence results using higher recursion theory
Arana, Andrew
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 1-8 / Harvested from Project Euclid
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We extend an independence result proved in [arana2]. We show that for all n, there is a special set of Πn sentences {φa}a∈ H corresponding to elements of a linear ordering (H,<H) of order type ω1CK(1+η). These sentences allow us to build completions {Ta}a∈ H of PA such that for a<H b, Ta ∩ Σn ⊂ Tb ∩ Σn, with φa∈ Ta, ¬φa ∈ Tb. Our method uses the Barwise—Kreisel Compactness Theorem.
Publié le : 2004-03-14
Classification:  
@article{1080938820,
     author = {Arana, Andrew},
     title = {Arithmetical independence results using higher recursion theory},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 1-8},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1080938820}
}

Arana, Andrew. Arithmetical independence results using higher recursion theory. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  1-8. http://gdmltest.u-ga.fr/item/1080938820/