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This sentence is false. For a trivial example, take Peano Arithmetic - its intended model is countable, but the upward Lowenheim-Skolem theorem guarantees we have models of every infinite cardinality. In particular, there is a model of Peano Arithmetic whose domain of discourse is uncountable. But, then this can't be the same domain of discourse as the intended model as the intended model is countable. So, that sentence in the article is wrong. —Preceding unsigned comment added by 217.43.149.136 ( talk) 21:44, 2 March 2010 (UTC)
Comments sought
"Most formal systems have many more models than they were intended to have (the existence of non-standard models is an example)." This sentence seems to need some edit. Isn't an unintended model just the same as a non-standard model? Then why is the latter just an "example" for the former one? Bbbbbbbbba ( talk) 11:47, 11 November 2010 (UTC)
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content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
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Text and/or other creative content from this version of Intended interpretation was copied or moved into Interpretation (logic) with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
This sentence is false. For a trivial example, take Peano Arithmetic - its intended model is countable, but the upward Lowenheim-Skolem theorem guarantees we have models of every infinite cardinality. In particular, there is a model of Peano Arithmetic whose domain of discourse is uncountable. But, then this can't be the same domain of discourse as the intended model as the intended model is countable. So, that sentence in the article is wrong. —Preceding unsigned comment added by 217.43.149.136 ( talk) 21:44, 2 March 2010 (UTC)
Comments sought
"Most formal systems have many more models than they were intended to have (the existence of non-standard models is an example)." This sentence seems to need some edit. Isn't an unintended model just the same as a non-standard model? Then why is the latter just an "example" for the former one? Bbbbbbbbba ( talk) 11:47, 11 November 2010 (UTC)