Zhen Lin

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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".
May 6	comment	Pole of differential $x / y$ is a rational function with a simple pole at infinity. Do you understand that calculation?
May 6	comment	Examples of epimorphisms which are not split epimorphisms? You mean coequaliser.
May 6	comment	What are the “ordinary” (e.g. arithmetic) consequences of the universe axiom? Yes, I am aware of Solovay's result. That does not count as a statement in ordinary mathematics to me.
May 6	awarded	Nice Question
May 5	answered	Determine whether two primitive recursive functions are equal
May 5	comment	Notation for Space of Multilinear Functions Strictly speaking, it would be an abuse of notation, but $\textrm{Hom}(V_1 \otimes \cdots \otimes V_p, W)$ is unambiguous...
May 5	comment	Confusion about cofinality Yes. But if $[0, \kappa)$ is the set of all ordinals of cardinality less than $\kappa$, then the answer is the same, provided the well-ordering principle is available.
May 4	comment	What's stronger: projective or locally free? flat or locally free? The question does not apply to general abelian categories, since there is no notion of "locally free" and no (obvious) notion of "flat".
May 4	comment	The Axiom of Choice and definability The inductive step is far too vague. Here is one problem: in the set-forming axioms, one can use parameters, so the "constant" terms must have variables. But once you allow that, then one can derive a form of meta-AC: suppose we have a proof of $\forall x . x \in X \to \exists y . y \in x$; then we can construct a definable term $c (x)$ such that $\forall x . x \in X \to c (x) \in x$; then by replacement, $\exists f . (f : X \to \bigcup X) \land \forall x . x \in X \to f (x) \in x$.
May 4	comment	The Axiom of Choice and definability My gut feeling is that your "Theorem" is false, because the same kind of reasoning can be used to "deduce" the axiom of choice. (See, for instance, the derivation of AC in Martin-Löf type theory.)
May 4	comment	$Pic(\mathbb{C}P^1)$ @ArthurStuart First of all, what is your definition of Picard group? If you are defining it as $H^1 (X, \mathscr{O}_X^{\times})$ then there's not going to be much chance of explaining it without sheaf theory!