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Let $\Phi(\bar x)$ be a type over a set $X$ with respect to a structure $A$. Show that if $\Phi$ is algebraic, then $\Phi$ contains a formula $\phi$ s.t. $A\models\exists\ _{ for some $\ n<\omega$.

I've really hit a wall with this one; I can only deal with the case $\Phi(\bar x)$ is a complete type. Any help is appreciated!

-Thanks

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    What's your definition of algebraic type? _This_ is the definition I'm familiar with...2012-12-10
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    I second Zhen's request for your definition of an algebraic type. I have seen precisely the property you want to prove used for that.2012-12-10
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    Clarification: A type Φ(x) over a structure A is algebraic if any tuple realising it is algebraic, but this includes any tuple in any elementary extension B of A.2012-12-10
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    And what is the definition of an algebraic tuple? I would say a tuple is algebraic if it realizes an algebraic type!2012-12-11
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    @Saeed: You probably wanted to say that the type is algebraic if *every* tuple realising it is algebraic.2012-12-11

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