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Results tagged with infinite-combinatorics
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user 103802
Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
2
votes
Independent families of functions on $\omega$ of size continuum
For (d) maybe the following was meant:
Take your independent family $F$ and partition it into continuum many families of size $\omega$:
$F = \{ I_{\alpha,n} : \alpha< \mathfrak{c},n \in \omega \}$ …
1
vote
Accepted
Existence of a specific mad family
You could define $\mathcal{A}$ recursively:
Enumerate all elements of $[2^{<\omega}]^\omega$ as $(X_\alpha)_{\alpha< \mathfrak{c}}$. Then whenever elements $(A_{\alpha})_{\alpha<\gamma}$ have alread …