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Transplendent models : Expansions omitting a type

Journal article
Authors Fredrik Engström
Richard W. Kaye
Published in Notre Dame Journal of Formal Logic
Volume 53
Issue 3
Pages 413-428
ISSN 0029-4527
Publication year 2012
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 413-428
Language en
Keywords models of arithmetic; resplendent models; standard cut; satisfaction classes
Subject categories Logic, Mathematical logic


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. We investigate two different formulations and prove necessary and suffcient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author's doctoral thesis.

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