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Results tagged with set-theory
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user 3969
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.
3
votes
Which topological spaces admit a nonstandard metric?
I once considered the following situation:
$[0;1]^X$ is metrizable (with values in $\mathbb{R}$), if $X$ is countable. So I wondered whether $[0;1]^\mathbb{R}$ is nonstandard-metrizable for some total …
- 11.1k
4
votes
1
answer
241
views
cardinality of local bases in the non-standard reals
Given a index set $S$ together with a ultrafilter $\mu$ on $S$ (such that no set of cardinality $< |S|$ has measure $1$). Let the ordered field $\mathbb{R}(S,\mu)$ denote the ultrapower of $\mathbb{R} …
- 11.1k
3
votes
Refinement-minimal intersecting covers
Disclaimer: This is not an answer, and just too long for a comment.
Here is an example why the chain condition does not hold (which does not mean that there are no refinement-minimal covers, just that …
- 11.1k