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Results tagged with set-theory
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user 8250
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.
6
votes
Accepted
MAD family with the choosability property
This answer only deals with the case that $R$ is infinite. I thought that I would be able to modify it to the finite case - thanks to Ilya Bogdanov for spotting the mistake in my argument. (His answer …
- 4,713
12
votes
BCT equivalent to DC
Wikipedia article on Baire category theorem and several other sources mention this paper: Blair, Charles E. The Baire category theorem implies the principle of dependent choices. Bull. Acad. Polon. Sc …
- 4,713
5
votes
Accepted
Bounding and domination numbers for relation $\leq$ modulo $\omega$-nullsets
The answer seems to be positive according to this paper: Barnabás Farkas, Lajos Soukup: The zero density ideal, cardinal invariants and related forcing problems.1
Theorem 2.3. If $\mathcal I$ is a …
- 4,713
4
votes
Accepted
Meeting a set of lines in $\mathbb{R}^n$
If we have a set $\mathcal L$ of lines in $\mathbb R^n$ such that $|\mathcal L|=\mathfrak c$, we can get the set $M$ with the desired properties using transfinite induction.
Take any well-ordering o …
- 4,713
4
votes
Accepted
Existence of maximal analytic P-ideal
As already mentioned in the comments, a free ultrafilter considered as a subset of Cantor space (or Cantor set) cannot be analytic, so the answer to the Question 1 is No. (Even without the assumption …
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8
votes
Accepted
Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mat...
A very good reference for various forms of AC is the book Howard, Rubin: Consequences of the Axiom of Choice, AMS, 1998. (See AMS website or Google Books.) This book contains a large database of vari …
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9
votes
Accepted
Is the Rudin-Keisler order of ultrafilters linear?
This would be more suitable as a comment, but I do not have enough reputation points.
Among the first results that google spits out for Rudin Keisler is the paper
Anatoly Gryzlov: On the Rudin-Keisle …
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1
vote
Is the isomorphism class of a fixed cardinality a set?
If I understand your question correctly, the first part can be rephrased as: Is the system of all sets of a given cardinality a set or a proper class.
It is a proper class already for singletons: Just …
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