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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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Diagonalization over a normal function and its derivatives on transfinite ordinals

Let $\Phi(0,\beta)$ a normal function from $On$ to $On$, and let $\Phi(\alpha,\beta)$ be the $\alpha$-th derivative of $\Phi(0,\beta)$. For example, let $\Phi(0,\beta)=\aleph_\beta$. Then, all functio …