Talk:Type (model theory)

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[edit] Example of a type

The example about \sqrt{2} confuses me. I have corrected the obvious problem: If x=\sqrt{2} (say, in reals) then for y smaller than -\sqrt 2 it is not true that y^2>2 \implies y>x (there is nothing about considering just positive reals in the article).

The definition of type that I know requests that if φ(x) and ψ(x) belong to the type in a certain model, then also \exists x (\phi(x) \wedge \psi(x)) holds in the model (that is, \phi \wedge \psi is consistent with the model). Thus, if the example statements about \sqrt 2 are meant as a type in model of rationals then we would need examples of two conditions that are also met by some rational number. Or maybe what is meant by the example is a type in the theory of arithmetics, because being consistent with a model of a theory and being consistent with a theory are differnt things?

I am not an expert on this, so a second opinion would be helpful.82.208.2.227 15:23, 25 September 2006 (UTC)

Two replies to the above. 1. As regards the example, it now reads y>0 \land y^2>2 \implies. 2. In general a (partial) type is not required to be a filter. Any (partial) type has however its set of concequences which is a filter of the set of formulae. I prefer to use (partial) types this way, it is not however totally standard. Something else: The word type is often used to mean complete type, and partial type is used for the general notion. Unfortunately there is not widespread agreement on this, different papers have a different convention. In my experience, the latter view of types being complete is more widespread, as in many areas one need only consider complete types. Comments? Thehalfone 10:25, 3 October 2006 (UTC)

1. Yes, I have corrected the example and noted it on the discussion page because I felt that a little explanation is in order. Sorry, if it confused anyone. I still think that the definitions could be cleared up a bit (preferably by an expert). 2. The lecture on logic that we have had (at Charles University, Prague) used the opposite convention. 82.208.2.227 20:07, 12 October 2006 (UTC)

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