Existentially Closed Structures and Godel's Second Incompleteness Theorem

Adamowicz, Zofia; Bigorajska, Teresa

J. Symbolic Logic, Tome 66 (2001) no. 1, p. 349-356 / Harvested from Project Euclid

Résumé

We prove that any 1-closed (see def 1.1) model of the $\Pi_2$ consequences of PA satisfies $\neg$Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.

Publié le : 2001-03-14
Classification:

@article{1183746375,
     author = {Adamowicz, Zofia and Bigorajska, Teresa},
     title = {Existentially Closed Structures and Godel's Second Incompleteness Theorem},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 349-356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746375}
}

Adamowicz, Zofia; Bigorajska, Teresa. Existentially Closed Structures and Godel's Second Incompleteness Theorem. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  349-356. http://gdmltest.u-ga.fr/item/1183746375/