Notre Dame Journal of Formal Logic

Transplendent Models: Expansions Omitting a Type

Fredrik Engström and Richard W. Kaye

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We expand the notion of resplendency to theories of the kind $T+p\!\!\uparrow $, where $T$ is a first-order theory and $p\!\!\uparrow $ 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.

Article information

Notre Dame J. Formal Logic Volume 53, Number 3 (2012), 413-428.

First available in Project Euclid: 24 September 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Secondary: 03C30: Other model constructions

models of arithmetic resplendent models standard cut satisfaction classes


Engström, Fredrik; Kaye, Richard W. Transplendent Models: Expansions Omitting a Type. Notre Dame J. Formal Logic 53 (2012), no. 3, 413--428. doi:10.1215/00294527-1716739.

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