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Results tagged with infinite-combinatorics
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user 38866
Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
5
votes
1
answer
333
views
Simultaneous failure of weak diamond
Let $\lambda$ be an infinite cardinal. Recall that Weak diamond $\Phi_S$ on $S\subseteq\lambda^+$ is the following principle:
For every function $F:2^{<\lambda^+}\rightarrow 2$, there exists $g\in 2^ …
- 2,381
7
votes
1
answer
424
views
On Consistency of an Existence
Let $\omega \leq \kappa <2^{\omega}$ , $\omega \leq\lambda \leq \kappa$ and $D(\kappa, \lambda)$ be the statement:
For all $ \mathfrak{B} \subseteq \mathbf{P}(\omega)$ with $|\mathfrak{B}|=\kappa$ t …
- 2,381
13
votes
2
answers
1k
views
On Hamkins' answer to a problem by Michael Hardy
Based on a post by Michael Hardy and Hamkins' answer to it Andreas Blass, Will Brian, Joel Hamkins, Michael Hardy and Paul Larson introduced a new cardinal characteristic of the continuum $\mathfrak{r …
- 2,381
3
votes
1
answer
290
views
Hausdorff's question on $\omega_1$-gap
I read here that the following problem of Hausdorff is apparently still open.
Is there a maximal branch $C$ in the poset $\omega^\omega$ with the eventual domination order, such that $C$ has no $\ …
- 2,381