If the resolution of an asymmetry requires restricting which set-theoretic operations preserve standardness, the resulting framework imposes new asymmetries rather than eliminating the original one.

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asymmetry(Modal logic frame semantics): A frame property expressible in hybrid logic by the formula c→□¬◇c, meaning if world x accesses world y, then y does not access x.
framework(Carnap's philosophy of language and logic): A structured system of rules or language that must be in place for rational discourse to be possible.
preserves(describing whether mathematical operations keep important qualities intact): To keep something the same or maintain a quality; in this context, to ensure that certain properties remain true when you apply an operation.
set-theoretic operations(describing mathematical tools used to manipulate groups of things): Mathematical procedures you perform on collections of objects (called 'sets'), like combining them, finding what they have in common, or removing items.

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