User blog comment:P進大好きbot/List of common mistakes on formal logic appearing in googology/@comment-44466522-20191230164711

Even if Rayo's number is well-defined from second order axioms, can't it take on different values in different models of set theory? For instance, wouldn't it have a different value if you are working in L than if you are working in a model containing 0#, since you can encode truth in L if 0# exists?