The above is the letter presenting the resignation of the editorial board of Topology, an Elsevier journal. The journal has been discontinued as of this year.

[…] As you are well aware, the Editors have been concerned about the price of Topology since Elsevier gained control of the journal in 1994. […] The journal Topology has an illustrious history with which we, on becoming editors, were extremely proud to be associated. […] However, we feel that Elsevier’s policies towards the publication of mathematics research have undermined this legacy.

Therefore, with great reluctance and sadness, we have made the difficult decision to resign. […]

On Google+, David Roberts gave a link to the journal’s site, with some highlights: As you can see here, the last published issue (vol. 48, 2-4) was June-December 2009. The previous issue was 40 pages and consisted of 2 papers (that you can purchase access to, at $31.50 each. Plus tax.) And there is also a supplement, published on December 2011. Only $31.50 (plus tax) for a 4 page correction.

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Yes. This is a consequence of the Davis-Matiyasevich-Putnam-Robinson work on Hilbert's 10th problem, and some standard number theory. A number of papers have details of the $\Pi^0_1$ sentence. To begin with, take a look at the relevant paper in Mathematical developments arising from Hilbert's problems (Proc. Sympos. Pure Math., Northern Illinois Un […]

I am looking for references discussing two inequalities that come up in the study of the dynamics of Newton's method on real-valued polynomials (in one variable). The inequalities are fairly different, but it seems to make sense to ask about both of them in the same post. Most of the details below are fairly elementary, they are mostly included for comp […]

Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]

Not necessarily. That $\mathfrak m$ is consistently singular is proved in MR0947850 (89m:03045) Kunen, Kenneth. Where $\mathsf{MA}$ first fails. J. Symbolic Logic 53(2), (1988), 429–433. There, Ken shows that $\mathfrak{m}$ can be singular of cofinality $\omega_1$. (Both links above are behind paywalls.)

Ignas: It is not possible to provide an explicit expression for a non-linear solution. The reason is that (it is a folklore result that) an additive $f:{\mathbb R}\to{\mathbb R}$ is linear iff it is measurable. (This result can be found in a variety of places, it is a standard exercise in measure theory books. As of this writing, there is a short proof here. […]

There are several nice proofs of the result. The most intuitive I'm aware of is the following: We may as well assume that $A$ and $B$ are disjoint. Consider the directed graph whose set of vertices is $A\cup B$, in which you add an edge from $a$ to $b$ precisely if $a\in A$, $b\in B$, and $f(a)=b$, or $a\in B$, $b\in A$, and $g(a)=b$. Now consider the c […]

A forcing collapses cardinals iff (by definition) some cardinal of the ground model is no longer a cardinal in the forcing extension. Naturally, this means that there is some $\kappa$ in the ground model whose cardinality in the extension is strictly smaller than $\kappa$ (e.g., let $\kappa$ be the first cardinal that witnesses the definition above). Note th […]

$\mathrm{HOD}$ always contains $L$ because any inner model contains $L$, by absoluteness. How easy it is to exhibit a difference really depends on your background. For instance, $0^\sharp$, if it exists, is a real that always belongs to $\mathrm{HOD}$ but is not in $L$. If you are not too comfortable with large cardinals, but know forcing, you may enjoy prov […]

The classical definition of $0^\sharp$ is as (the set of Gödel numbers of) a theory, namely, the unique Ehrenfeucht-Mostowski blueprint satisfying certain properties (coding indiscernibility). This is a perfectly good definition formalizable in $\mathsf{ZFC}$, but $\mathsf{ZFC}$ or even mild extensions of $\mathsf{ZFC}$ are not enough to prove that there are […]

This is the descriptor operator. $(\iota x)\varphi x $ is the unique $x $ with the property specified by $\varphi $ (should it be the case that, indeed, there is precisely one such $x $). The Wikipedia entry on Principia has a very decent explanation of their notation.

[…] E. Caicedo: A letter (on the resignation of the editorial board of […]