Notre Dame Journal of Formal Logic

Transplendent Models: Expansions Omitting a Type

Fredrik Engström and Richard W. Kaye

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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

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

Keywords
models of arithmetic resplendent models standard cut satisfaction classes

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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References

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