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Results tagged with set-theory
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user 517040
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.
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 …
- 300
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 $\ …
- 300