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Results tagged with set-theory
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user 17798
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.
2
votes
Accepted
Injective choice function for infinite complete linear hypergraphs
After the discussion above, here is what I think is the cleanest proof and it has the property that $f$ is bijection (unless there is an edge of order 1).
If there is an edge of order 1, then we must …
- 1,701
3
votes
Induced subgraphs of the almost-disjointness graph
My first thought for the case where $|V|\leq \aleph_0$ is that surely the Rado graph can be constructed as an induced subgraph of $([\omega]^{\omega}, E)$ (since the Rado graph contains a copy of ever …
- 1,701
4
votes
Accepted
Is König's Property for graphs inheritable from finite subgraphs?
(Just making my comment an answer as suggested.)
If every finite subgraph of $G$ satisfies Kőnig's Property, then $G$ has no odd cycles and is thus bipartite. Aharoni
(König's Duality Theorem For Infi …
- 1,701