I am reading notes on finite model theory and I came across a notion of a vocabulary. What is it? I tried searching on the internet but did not find anything relevant.

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    $\begingroup$ The non-logical symbols of the language, also called signature or vocabulary. $\endgroup$ – Mauro ALLEGRANZA Sep 29 '18 at 11:00
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    $\begingroup$ Also called a language. We have way too many names for some things. (@MauroALLEGRANZA You should turn your comments into an answer.) $\endgroup$ – Noah Schweber Sep 29 '18 at 19:45

See Leonid Libkin, Elements of Finite Model Theory, Springer (2012), page 13 :

Definition 2.1 A vocabulary $σ$ is a collection of constant symbols (denoted $c_1,\ldots, c_n,\ldots$), relation, or predicate, symbols ($P_1,\ldots,P_n,\ldots$) and function symbols ($f_1,\ldots,f_n,\ldots$). Each relation and function symbol has an associated arity.

Is the set of non-logical symbols of the language, also called signature.


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