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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.

Tim
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1 Answers1

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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.

Mauro ALLEGRANZA
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