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1d
reviewed Approve Spectral theory of $\frac{\partial ^2}{\partial x^2} + \frac{\partial ^2}{\partial y^2}$ and $4 \frac{\partial ^2}{\partial z\partial \bar{z}}$
1d
comment irrationality of the p-adic exponential
But do you have a simple/elementary proof of the fact that $log(1+p)$ is irrational? Or of the fact that $log(1+x)$ is irrational for every rational $p$-adic $x$ such that $|x|<1$? (the latter would of course answer OP's question) I'd love to see a short and simple proof of the irrationality of just about any $p$-adic "of this sort" (and that is, in fact, transcendental).
2d
awarded  Custodian
2d
reviewed Reviewed A finiteness property for semi-simple algebraic groups
2d
comment an algebraic variety for a boolean circuit
@Alexey Yes, that also works: you get a variety that is isomorphic to an open set (namely $\{(\forall j)\,f_j\neq 1\}$) of $\mathbb{A}^n$, hence also smooth and geometrically irreducible like the one I proposed. The main difference with the one I proposed is you get the equivalence with only a specific value of the $y_j$, not with any; but if that's fine with you, of course, it's simpler.
2d
answered Self-containing trees
2d
comment Self-containing trees
I suspect your tree is strongly related to the sort of things studied in this paper (see esp. figure 5 on p. 9).
2d
comment Self-containing trees
How do you remove duplicates? Or more precisely, if $rx = x'+1$, how do you decide whether to connect this node, which you want to make unique, to $x$ or to $x'$? Do you always make the same choice, or are you asking for any system of choices?
2d
answered an algebraic variety for a boolean circuit
Apr
27
reviewed Approve End points of continua
Apr
27
comment When a ring is a polynomial ring?
This is a difficult problem, even when $R$ is a finitely generated subring of a ring of polynomials. You shouldn't expect a definite answer. You might like to have a look at van den Essen's "Seven Lectures on Polynomial Automorphisms" (in id. ed., Automorphisms of Affine Space (Curaçao 1994), Springer 1995), or his book Polynomial Automorphisms and the Jacobian Conjecture (Birkhäuser 2000).
Apr
26
reviewed Approve Reference for algebraic manipulation of sheaves
Apr
26
comment irrationality of the p-adic exponential
A good start might be to examine the proof of the classical fact that the last nonzero digit of $n!$ is not (pre)periodic in any base. (I'm not saying one implies the other, but they certainly seem related.) I thought there were proofs of that fact all over the Internet but for some reason I seem to have wandered into a parallel universe where there are none. Perhaps it's easier to prove the irrationality of $\sum n!$ or $\sum n! p^n$ for a start (I wonder if these have a name?).
Apr
26
revised irrationality of the p-adic exponential
call the quantity e^p to avoid confusion
Apr
25
revised Computing the ordinal of a rational language well-partially-ordered by the subword relation
cite de Jongh & Parikh's paper properly, and add two comments
Apr
24
comment Are there any results on well-quasi-ordering of languages?
I think this is wrong in general: it is precisely the difference between the "well-quasi-order" (wqo) and the "better-quasi-order" (bqo) properties (see, e.g., arXiv:math/0601119 by Pouzet and Sauer) that bqo passes from $E$ to $\mathcal{P}(E)$ whereas wqo in general does not. However, $A^*$ is indeed bqo by a result of Nash-Williams (somewhere in his 1963–1968 papers) so I agree with the conclusion.
Apr
24
asked Computing the ordinal of a rational language well-partially-ordered by the subword relation
Apr
24
awarded  Custodian
Apr
24
reviewed Approve Applications of space filling curves
Apr
22
comment Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
(contd.) In the online version of the same text, the same statement (now in §1.3.2) is referred to a preprint called "Suitable extender sequences (July, 2009)". The papers published in 2010–2011 in J. Math. Logic are called "Suitable extender models" (emphasis mine), and the date suggests that they were published in time for the reference to be fixed in the survey article I mentioned: so is Woodin referring to yet another paper? So many mysteries.