Reputation
44,075
Next tag badge:
93/100 score
27/20 answers
Badges
2 53 128
Newest
 Enlightened
Impact
~368k people reached

May
11
comment Space modelled on ring
Do you mean a scheme?
May
10
comment A question about partitioning the unit cube into simplexes
There is a triangulation of the $n$-cube satisfying condition (1): it is what is obtained by considering the simplicial set $(\Delta^1)^n$. I haven't thought about (2).
May
9
comment Axiom of Choice-esque argument to show that a proof of a statement exists without actually giving a proof
Any such category or topological space must be connected: everything proves $\top$, and $\bot$ proves everything.
May
9
comment Is $\mathbb{N}$ impossible to pin down?
If you believe that there is a "real" $\mathbb{N}$, then it sounds like you've pinned it down already!
May
8
comment $C(X) \cup C(Y) = C(X \cup Y)$ if $C$ is an algebraic closure and $X, Y$ are finite?
The smallest closed subset containing $C(X)$ and $C(Y)$ is $C(X \cup Y)$. But in general that is not $C(X) \cup C(Y)$.
May
7
answered Existence of not locally small categories
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
Hmmm... yes, I suppose that is true. Do you have a better proof for the plane curve case, then?
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
Well, if if $h$ is a rational function, then there are some coprime $F$ and $G$ such that $h = F / G$. If they weren't of degree $1$ then that would contradict the condition on the degrees of the divisors.
May
7
comment Is a divisor in the hyperplane class necessarily a hyperplane divisor?
If $F$ and $G$ are homogeneous of degree $m$ and coprime, then $F / G$ will be a rational function with $m \deg H$ zeros and $m \deg H$ poles, counted with multiplicity, by Bézout's theorem.
May
7
comment Can “proving mathematical theorems” as a 1 player puzzle be studied in combinatorial game theory?
See Wikipedia about game semantics.
May
7
comment Can “proving mathematical theorems” as a 1 player puzzle be studied in combinatorial game theory?
Actually, it's a two-player game between the verifier and the refuter.
May
6
asked Is a divisor in the hyperplane class necessarily a hyperplane divisor?
May
6
comment Existence of not locally small categories
If those authors don't admit the existence of locally small categories, why would they talk about such things? To talk about such things would require them to admit there are categories that are not locally small! But one sometimes speaks of ‘metacategories’.
May
6
comment formalized provability predicate and implication relation
If your formal proof system is reasonable, then yes. (Here is an example of an unreasonable proof system: no axioms, no rules of inference. Nothing is provable.)
May
6
awarded  Caucus
May
6
comment Existence of not locally small categories
The point is that there are people who take ‘category’ to mean locally small by definition. So for them a category that is not locally small does not exist – by definition!
May
6
comment Existence of not locally small categories
Well, the collection of all sets is certainly well-defined, yet some people say such a thing does not exist. The question is of "legitimacy" more than whether we can define it at all.
May
6
comment Irreducible closed subsets of projective varieties
Well, it is certainly the case that every closed irreducible subset of a projective variety is a projective variety. But if your definition of "projective variety" does not include irreducibility then even every closed subset of a projective variety is a projective variety. Therefore if $Y$ has a irreducible closed subset that is not a projective variety, then $Y$ cannot be projective.
May
6
comment Pole of differential
That's not correct. Both $x$ and $y$ evaluate to $\infty$ at $[0 : 1 : 0]$. (Otherwise $x$ and $y$ would be functions that are regular everywhere on a projective variety, hence, constant – an absurdity.)
May
6
comment Irreducible closed subsets of projective varieties
Some people include irreducibility in their definition of "variety".