3
$\begingroup$

I cannot figure out the solution to this exercise in Marker. Can someone help me?

$(Z \oplus Z, +, 0) \not\equiv (Z, +, 0)$

  • 3
    It's hard to tell without the text what the question is. Perhaps the problem is to show these models are not $f$irst-order equivalent in the language of + with identity 0, i.e. to find a first-order sentence satisfied in one but not the other model?2011-03-17

1 Answers 1

10

EDIT: The sentence $\exists z \forall y \exists x (x+x=y \vee x+x+z=y)$ is true in $\mathbb{Z}$ but not in $\mathbb{Z} \oplus \mathbb{Z}$.

  • 0
    Thank you very much for your fast response.2011-03-17