Lindström's theorem characterizes logics up to expressive equivalence over unrestricted signatures, but many-sorted logic operates over typed signatures that are not freely interchangeable with single-sorted ones.

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Expressive equivalence(as a comparison between logical systems): When two different logical systems can say or prove all the same things—they're equally powerful in what they can express.
Lindström's theorem(mathematical logic): A famous mathematical result (named after Swedish logician Per Lindström) proving that first-order logic is the strongest logic that can keep certain desirable properties—if you make it more powerful, you have to give something up.
Signature (in logic)(The shape or structure of a logical system's basic components): The basic building blocks or vocabulary that a logical system uses, like the symbols, relations, and operations you're allowed to work with.
Single-sorted logic(as a contrast to many-sorted logic): A logical system that treats all objects the same way without dividing them into separate categories or types.

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