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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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closed as off-topic by Emil Jeřábek, David White, Ramiro de la Vega, Ricardo Andrade, Vidit Nanda Oct 4 '13 at 17:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Emil Jeřábek, David White, Ramiro de la Vega, Ricardo Andrade, Vidit Nanda
If this question can be reworded to fit the rules in the help center, please edit the question.

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? – supercooldave Jun 23 '10 at 15:22
Please expand the question (using the "edit" link) with some explanation of your specific goals. – S. Carnahan Jun 23 '10 at 15:36
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. – François G. Dorais Jun 23 '10 at 16:19
-1 as per Scott's comment, though if this is edited soon I'm happy to reverse/rescind the downvote. – Yemon Choi Jun 24 '10 at 5:16
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. – ps_ttf Oct 3 '13 at 12:27
up vote 3 down vote accepted

To the best of my knowledge, there are no deep historical or mathematical connections between these two uses of the term type.

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(Just to make my comment an answer.) – François G. Dorais Oct 3 '13 at 13:54

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