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Results tagged with set-theory
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user 1306
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.
35
votes
Injectivity implies surjectivity
There is an improvement of the answer of Joseph Van Name which I feel is much more in the spirit in the question asked:
Let $(X,d)$ be a compact metric space, and assume that the mapping $f\colon X\t …
- 53.3k
3
votes
Non-Formal Applications: Higman and Kruskal
Unsurprisingly, there are various ways in which Higman's lemma is used in the context of Gröbner bases. One interesting recent example : http://www.msri.org/people/members/chillar/files/HS-MonoidGBFin …
- 16.9k
43
votes
Accepted
Is there a natural bijection from $\mathbb{N}$ to $\mathbb{Q}$?
There is a following result which is quite lovely, I think (I don't remember right away whose result this is):
Let us define a function $f\colon\mathbb{N}\to\mathbb{Q}^+$ as follows: $f(1)=1$, and al …
- 16.9k