If the ambient theory used to construct such models itself requires large cardinal assumptions or AC, the argument is question-begging against anti-choice foundationalists like Solovay.

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Key Terms

AC (Axiom of Choice)(as used in set theory): A basic assumption in mathematics that allows you to make infinitely many arbitrary choices all at once—something that seems obvious but is actually quite controversial.
Ambient theory(in mathematical logic and philosophy of mathematics): The underlying mathematical framework or system of assumptions that a scientist or mathematician uses as their foundation when building models or arguments.
Anti-choice foundationalists(in philosophy of mathematics): Philosophers and mathematicians who reject the Axiom of Choice and believe mathematics should be built on foundations that don't require assuming it.
Large cardinal assumptions(as used in set theory): Extra mathematical assumptions beyond the standard rules that assert the existence of very large, powerful sets with special properties.

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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.

If the ambient theory used to construct such models itself requires large cardinal assumptions or AC, the argument is question-begging against anti-choice foundationalists like Solovay.

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