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What is the simplest way to say "$\varphi$ is a well-formed formula of formal system $\mathbf{F}$" in symbols? The only thing that comes to mind is: $$\varphi \in \mathbf{F}$$

Am I right?

I.e., would it be acceptable to say (somewhat cumbersomely): $$'\exists x (x=x)'\in \mathbf{ZFC}$$

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  • $\begingroup$ It depends on the definition of Formal system ... $\endgroup$ – Mauro ALLEGRANZA Apr 14 '16 at 13:17
  • $\begingroup$ @MauroALLEGRANZA I have the most common definition in mind. $\endgroup$ – Constantine Apr 14 '16 at 13:22
  • $\begingroup$ Usually, a Formal system F is made of : (i) an alphabet (set of symbols); (ii) a grammar, i.e. a set of rules specifying the well-formed expressions; (iii) a set of axioms; (iv) a set of inference rules. If so, to say $\varphi \in$ F is ambiguous. $\endgroup$ – Mauro ALLEGRANZA Apr 14 '16 at 13:25
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    $\begingroup$ Your definition will be correct provided a formal system is a set of wffs. I do not think that is the most common definition. Why do you need to say "φ is a well-formed formula of formal system F" in symbols? Would it not be getter (and clearer) to say it in words? $\endgroup$ – GEdgar Apr 14 '16 at 13:25
  • $\begingroup$ The simplest and best way is this: "$\phi$ is a wff of the formal system $F$". $\endgroup$ – David C. Ullrich Apr 14 '16 at 13:44

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