## Notre Dame Journal of Formal Logic

### Transplendent Models: Expansions Omitting a Type

#### Abstract

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

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

Dates
First available in Project Euclid: 24 September 2012

https://projecteuclid.org/euclid.ndjfl/1348524119

Digital Object Identifier
doi:10.1215/00294527-1716739

Mathematical Reviews number (MathSciNet)
MR2981016

Zentralblatt MATH identifier
1258.03041

Subjects
Secondary: 03C30: Other model constructions

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1348524119

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