A model of peano arithmetic with no elementary end extension

Journal of Symbolic Logic 43 (3):563-567 (1978)
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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