Other than $\models$, is there standardized notation for semantic consequence? It is common practice to use $\models$ both for the satisfaction relation between models and sentences, and for the corresponding semantic consequence relation. **Question.** Suppose I don't want to use $\models$ for semantic consequence (personally, I think this particular convention causes more confusion than its worth), what should I use instead? In particular, is there a standardized alternative?

In Ben-Gurion University, where I did my B.Sc. and M.Sc. we used $T\implies\varphi$ to denote logical implication, which was really a semantic property:

> $T\implies\varphi$ if and only if for every interpretation for the language $M$ and assignment $s$ for $M$, such that every formula in $T$ is true under that assignment; $\varphi$ is true under $s$ as well.

This makes all the more reason to pay attention as to what is $\implies$ and what is $\rightarrow$ (statement about propositions vs. a connective in the language).