Full Idea
Nonstandard models of Peano arithmetic are models of PA that are not isomorphic to the standard model. Their existence can be established with the compactness theorem or the adequacy theorem of first-order logic.
Gist of Idea
The compactness theorem can prove nonstandard models of PA
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 8.3)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.83
Related Ideas
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