I know that for the complete theory $Th((\mathbb{Q},+,0))$ we have the prime model $(\mathbb{Q},+,0)$ and the countable saturated model $(\mathbb{Q}^{\infty},+,0)$, but what should I do when I try to prove this claim? Do I have to use the Ehrenfeuch-Fraisse Method?
Look up to the complete theory $Th((\mathbb{Q},<,0,1))$. I have to prove that there exists five 1-types of this theory, but that proves only that there are at least five 1-types, but how I have to prove that there exists precisly five 1-types?! I think I have to pick a arbitrary model of the theory and have to embed this into $(\mathbb{Q},<,0,1)$. Is this true? Can someone help me?
Thank you :)