Lindström's theorem establishes that classical FOL is maximal for compactness plus Löwenheim-Skolem, but XL's sort structure introduces expressive additions that may escape this maximality boundary.

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Expressive(as a quality of a logical system): Able to communicate or represent a wide range of ideas, meanings, or logical statements; capable of saying what needs to be said.
First-order logic (FOL)(the logical system being discussed): A formal system for reasoning where you can make statements about objects and their properties, but you can't directly make claims about claims themselves—it's the most common 'language' logicians use to study reasoning.
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.
Löwenheim-Skolem property(One of the two key properties used in Lindström's characterization of first-order logic.): A property of a logic whereby if a sentence or theory has a model, it has a model of at most countable cardinality (downward form); used here as a constraint on the strength of a logic.

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