An incompleteness theorem for βn-models
Mummert, Carl ; Simpson, Stephen G.
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 612-616 / Harvested from Project Euclid
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Let n be a positive integer. By a βn-model we mean an ω-model which is elementary with respect to Σ1n formulas. We prove the following βn-model version of Gödel’s Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a βn-model of S, then there exists a βn-model of S + “there is no countable βn-model of S”. We also prove a βn-model version of Löb’s Theorem. As a corollary, we obtain a βn-model which is not a βn+1-model.
Publié le : 2004-06-15
Classification:  
@article{1082418545,
     author = {Mummert, Carl and Simpson, Stephen G.},
     title = {An incompleteness theorem for $\beta$<sub>n</sub>-models},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 612-616},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082418545}
}

Mummert, Carl; Simpson, Stephen G. An incompleteness theorem for βn-models. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  612-616. http://gdmltest.u-ga.fr/item/1082418545/