Intuitive understanding of definitional expansion in model theory
0
1
$begingroup$
I was trying to understand what definitional expansion mean. Consider having two L-structures $mathcal A$ and $mathcal A'$ where $A'$ is an L'-expansion of $mathcal A$ . We way that $mathcal A'$ is a definitional expansion of $mathcal A$ if for each symbol $s in L' setminus L$ the interpretation of $s^{mathcal A'}$ of $s$ in $mathcal A'$ is 0-definable in $mathcal A$ . I understand what zero definable for a set is, which means: $$ varphi^{mathcal A} = { (a_1,...,a_m) in A^m mid mathcal A models varphi(a_1,...,a_m)}$$ when its zero definable the L-formula $varphi$ is only in terms of $L$ (and not the names of the elements of the underlying set $a in A$ ). However in this context we have a single element. We say its zero definable ok perhaps that means t...
