$\begingroup$In Ebbinghaus' Mathematical Logic, II.2.1 on p14 says that the alphabet of a first order language contains function symbols, relation symbols, and constants, whereas I don't see these symbols in "the alphabet of the language of propositional logic" in XI.4.1 on p201.
So is it true that "the alphabet of the language of propositional logic" has no function symbols, relation symbols, and constants?
By "the" in "the alphabet of the language of propositional logic", is there only one language of propositional logic, while there are many first order languages?
Thanks.
$\endgroup$1 Answer
$\begingroup$Exactly. Propositional logic has only propositional variables and connectives (and parentheses).
See page 201, Def.4.1.
You may have different languages according to the set of basic connectives used.
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