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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.

11 votes

Extracting a common convergent indexing from an uncountable family of sequences

Using notation by the answer by Hamkins, I'll prove that $\mathbb c_{\mathbb R}\ge\min\{\mathfrak s,\mathfrak b\}$. Thanks to Theorem 8.11 of Halbeisen's book Combinatorial Set Theory, we know that $\ …
alvoi's user avatar
  • 300
9 votes

Extracting a common convergent indexing from an uncountable family of sequences

We prove that $\mathbb c=\mathbb c_{\mathbb R}$: clearly $\mathbb c\le\mathbb c_{\mathbb R}$ holds, hence it is enough to prove $\mathbb c\ge\mathbb c_{\mathbb R}$. This means: for all reflexive separ …
alvoi's user avatar
  • 300