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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
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Existence of a set of valid Busy-Beaver entries.
In reference to 1961 paper "On Non Computable Functions" by T. Rado.
Motivation - Scott Aaronson's Who Can Name the Bigger Number?.
M is an n-state binary Turing machine. A valid BB-n entry is a …