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Results tagged with set-theory
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user 161756
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.
1
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0
answers
180
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Partition $\mathfrak c$-dense set to $\mathfrak c$- many dense set
A subset of $A\subset\mathbb R$ is called $\mathfrak c$-dense if $ |A\cap I|=\mathfrak c$ for any none open interval $I\subset\mathbb R.$ Then, there is a partition for $A$ to continuum many dense s …
- 179
4
votes
0
answers
175
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Construction of a function by transfinite recursion
Let $\mathcal F:=\{f_\xi\colon \xi<\mathfrak c\}$ be a family of functions from $\Bbb R$ to $\Bbb R$ and $K$ be a nonempty perfect set. The question is
Construct a function $g\colon \Bbb R \to \Bbb R …
- 179