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main.tex

@@ -107,7 +107,6 @@ where $\bar X$ denotes a $d$-tuple of monadic variables.
 Given a structure $A$ over $\ssign$, we define its image by $T$ by a structure $B=\sem T(B)$ over $\tsign$: the universe of $B$ is the set $U=\set{\bar S\mid\ A \models \phi_U(\bar S)}$, given $R\in \tsign$ of arity $k$, we define $R$ in $B$ as the set $\set{\tuple{\bar S_1,\ldots,\bar S_k}\in U^k\mid\ \phi_R(\bar S_1,\ldots,\bar S_k)}$.
 %Given tuples $\bar X_1,\ldots,\bar X_l$, we extend $\sem T$ by $\sem T(A,\bar X_1,\ldots,\bar X_l)=B,\set{\bar X_1},\ldots,\set{\bar X_l}$.
 
-\fomi is defined by restricting formulas to be in \fo.
 
 A non-deterministic \msomi (\nmsomi) $S$ from $\ssign$-structures to $\tsign$-structures with $k$ parameters is given by an \msomi $T$ from $\ssign\uplus\set{X_1,\ldots,X_k}$-structures to $\tsign$-structures where $X_1,\ldots,X_k$ are additional unary symbols. Let $\pi$ denote the natural projection from $\ssign\uplus\set{X_1,\ldots,X_k}$-structures to $\ssign$-structures. We define $\sem S(A)=\set{\sem T(C)\mid\ \pi(C)=A}$.