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bio website dorais.org
location Burlington, VT
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visits member for 5 years, 9 months
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I like math and a few other things...


Aug
22
revised Minimum size of the union of sets
added a summary
Aug
22
answered Minimum size of the union of sets
Aug
22
comment Minimum size of the union of sets
When $p=1$, the requirement says that $\{S_1,\ldots,S_k\}$ is a Sperner Family. Sperner's Theorem then says that if $n = |S_1 \cup \cdots \cup S_k|$ then $k \leq \binom{n}{\lfloor n/2 \rfloor}$, which is optimal. Asymptotically $\binom{n}{\lfloor n/2 \rfloor}$ is $2^n\sqrt{2/\pi n}$, which can be used to get bounds.
Aug
20
comment Hedetniemi's conjecture for graphs with countable chromatic number
Excellent! What a wonderful argument! As a consequence, the function $h$ at the end of my answer must be unbounded.
Aug
20
revised Hedetniemi's conjecture for graphs with countable chromatic number
addendum
Aug
20
answered Hedetniemi's conjecture for graphs with countable chromatic number
Aug
18
awarded  Nice Question
Aug
15
comment “set of all irreducible representations of a group”, set-theoretic issues
You don't need to make one universal choice from every class, you can make a nonempty set of choices from each class. Scott's Trick is a systematic way of doing this in ZF and in Bourbaki's system: en.wikipedia.org/wiki/Scott%27s_trick
Aug
11
awarded  Popular Question
Jul
23
awarded  Notable Question
Jul
1
revised What is the reverse mathematical strength of the fundamental theorem of algebra?
small correction
Jul
1
revised What is the reverse mathematical strength of the fundamental theorem of algebra?
added 543 characters in body
Jul
1
answered What is the reverse mathematical strength of the fundamental theorem of algebra?
Jun
28
comment Largest symmetric matrix given rank
Wouldn't the adjacency matrix of a graph also have zeros on the diagonal?
Jun
28
revised Preserving $\omega_1$ is Inaccessible to the reals
fixed grammar
Jun
26
comment Type theory: can multiple elimination rules be defined, in principle?
You may end up with two terms that are 'visibly identical' but not definitionally equal unless you add more rules to fix this. Why not define the first as a special case of the second? Derived rules are fine...
Jun
26
comment Type theory: can multiple elimination rules be defined, in principle?
The elimination rule for nat in dependent type theory has C being a type family over nat and both your elimination rules are special cases of that one.
Jun
11
revised methods for situations where well-posedness criteria hold but global solutions do not exist
edited tags
Jun
10
comment “Family Tree” of Theorems
@YoavKallus Sorry, I misread your description of the arrows. I guess you mean the equivalences rather than the strict implications.
Jun
9
comment “Family Tree” of Theorems
@YoavKallus: Double arrows usually mean that the converse implication is known to be false. Dependency is very hard to define rigorously. The connection is that if $A$ really depends on $B$ then it must be that $B$ implies $A$. Otherwise, we could use something strictly weaker than $A$ to prove $B$. (For example, $A \lor B$ could be used instead of $A$.) There doesn't seem to be any other purely mathematical ways of defining "dependency". There are, of course, historical and sociological ways to define dependency that behave differently.