Possible worlds semantics identifies propositions with sets of possible worlds, but this framework provably cannot distinguish logically equivalent mathematical truths like Fermat's Last Theorem from Goldbach's Conjecture.

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Fermat's Last Theorem(as a specific mathematical statement being used as an example): A famous math problem (now proven true) stating that certain equations with whole numbers have no solutions—it puzzled mathematicians for 358 years.
Goldbach's conjecture(Remains unproved as of the time of writing; used as the running example for discussion of partial descriptions and algorithmic complexity.): The conjecture, stated in 1742, that every even integer greater than 2 can be expressed as the sum of two prime numbers.
logically equivalent(used to describe when different phrasings express the identical logical claim): Two statements are logically equivalent when they mean exactly the same thing and must always have the same truth value (both true or both false).
possible worlds semantics(Philosophy of language): A propositionalist approach that identifies propositions with sets of possible worlds.

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