# Model theory basic definitions

1. Sep 19, 2010

### ibc

Hey
I've been reading the basic definitions for model theory, and got a bit confused, maybe someone can help me?

That's how I understood the definitions:
An m-Type in a model M is a set of formulas (with m variables), such that it is finitely satisfiable
An m-Type over A in M is a set of formulas (with m variables) in the language that includes personal constants for all the terms in A, such that it is finitely satisfiable

M is $$\lambda$$-compact if any type in M with cardinality smaller than $$\lambda$$ is fulfilled in M.
M is $$\lambda$$-saturated if any type over A in M, such that the cardinality of A is smaller than $$\lambda$$ is fulfilled in M.

So the way it seems: a structure which is 0-saturated is $$\lambda$$-compact for all $$\lambda$$?

Is there something wrong with my conclusion?
Is there something wrong with the definitions?

Thanks