Solovay's 1970 model demonstrates that all sets of reals can be Lebesgue measurable assuming an inaccessible cardinal, undermining the claim that well-foundedness alone drives well-orderability.

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Lebesgue measurable(as a mathematical property in measure theory): A property that allows a set of numbers to have a well-defined 'size' or 'measure,' similar to how we can measure the length of a line segment.
Model (in logic)(in formal logic and semantics): An imaginary scenario or description of a possible world where certain statements are true or false—used to test whether logical arguments work.
Sets of reals(as a mathematical object): Collections of real numbers (the everyday numbers we use, including whole numbers, fractions, and decimals).
Solovay: # Solovay Robert Solovay is an American mathematician best known for his groundbreaking work in logic and set theory, particularly his proof that certain mathematical statements cannot be proven true or false using standard axioms. His work is important because it revealed fundamental limits to what mathematics can prove, influencing how mathematicians understand the foundations of their field.

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