Is there any connection between the definition of type in model theory and the definitions from type theory? Is there any explanation why the same term is used for these notions, maybe in the historical sense.
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1$\begingroup$ The question is too vague. On the surface, the two concepts are quite different. But the notion of type in model theory is very general, so types (in type theory) probably can be modelled by types (in model theory), but this is unlikely to be very interesting. What do you want to learn from answers to this question? $\endgroup$– supercooldaveJun 23, 2010 at 15:22
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1$\begingroup$ Please expand the question (using the "edit" link) with some explanation of your specific goals. $\endgroup$– S. Carnahan ♦Jun 23, 2010 at 15:36
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$\begingroup$ There is no historical connection between these two uses of the term type. That said, types in type theory naturally correspond to incomplete types (the sorts) for the associated multi-sorted first-order language. $\endgroup$– François G. DoraisJun 23, 2010 at 16:19
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$\begingroup$ -1 as per Scott's comment, though if this is edited soon I'm happy to reverse/rescind the downvote. $\endgroup$– Yemon ChoiJun 24, 2010 at 5:16
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$\begingroup$ Thank you for the responses. It was posted a long time ago already, but I think that the answer from Francois is good enough. I've updated the question. $\endgroup$– ps_ttfOct 3, 2013 at 12:27
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To the best of my knowledge, there are no deep historical or mathematical connections between these two uses of the term type.
answered Oct 3, 2013 at 13:54
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$\begingroup$ (Just to make my comment an answer.) $\endgroup$ Oct 3, 2013 at 13:54