A Model of Peano Arithmetic with no Elementary End Extension
Mills, George
J. Symbolic Logic, Tome 43 (1978) no. 1, p. 563-567 / Harvested from Project Euclid
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We construct a model of Peano arithmetic in an uncountable language which has no elementary end extension. This answers a question of Gaifman and contrasts with the well-known theorem of MacDowell and Specker which states that every model of Peano arithmetic in a countable language has an elementary end extension. The construction employs forcing in a nonstandard model.
Publié le : 1978-09-14
Classification:  
@article{1183740261,
     author = {Mills, George},
     title = {A Model of Peano Arithmetic with no Elementary End Extension},
     journal = {J. Symbolic Logic},
     volume = {43},
     number = {1},
     year = {1978},
     pages = { 563-567},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183740261}
}

Mills, George. A Model of Peano Arithmetic with no Elementary End Extension. J. Symbolic Logic, Tome 43 (1978) no. 1, pp.  563-567. http://gdmltest.u-ga.fr/item/1183740261/