Journal of Symbolic Logic 43 (3):563-567 (1978)
| Abstract |
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
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| DOI | 10.2307/2273532 |
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References found in this work BETA
Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Citations of this work BETA
A Standard Model of Peano Arithmetic with No Conservative Elementary Extension.Ali Enayat - 2008 - Annals of Pure and Applied Logic 156 (2):308-318.
Models of Expansions of Equation Image with No End Extensions.Saharon Shelah - 2011 - Mathematical Logic Quarterly 57 (4):341-365.
Minimal Elementary Extensions of Models of Set Theory and Arithmetic.Ali Enayat - 1990 - Archive for Mathematical Logic 30 (3):181-192.
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