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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 [tex]\lambda[/tex]-compact if any type in M with cardinality smaller than [tex]\lambda[/tex] is fulfilled in M.

M is [tex]\lambda[/tex]-saturated if any type over A in M, such that the cardinality of A is smaller than [tex]\lambda[/tex] is fulfilled in M.

So the way it seems: a structure which is 0-saturated is [tex]\lambda[/tex]-compact for all [tex]\lambda[/tex]?

Is there something wrong with my conclusion?

Is there something wrong with the definitions?

Thanks

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# Model theory basic definitions

Can you offer guidance or do you also need help?

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