Transplendent Models: Expansions Omitting a Type

Notre Dame Journal of Formal Logic 53 (3):413-428 (2012)
Abstract
We expand the notion of resplendency to theories of the kind T+p↑, where T is a first-order theory and p↑ expresses that the type p is omitted; both T and p are in languages extending the base language. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA.
Keywords models of arithmetic   resplendent models   standard cut   satisfaction classes
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