Studia Logica: An International Journal for Symbolic Logic, not too long ago revealed after which retracted two articles by Janusz Czelakowski (Opole) following a dialogue at MathOverflow, a web site for skilled mathematicians.
The articles are “The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic” and “There are Infinitely Many Mersenne Prime Numbers. Applications of Rasiowa–Sikorski Lemma in Arithmetic“, each revealed on October twenty fifth.
The primary article drew the eye of MathOverflow due to its ambitiousness. Right here is its summary:
The paper is worried with the outdated conjecture that there are infinitely many twin primes. Within the paper we present that this conjecture is true, that’s, it’s true in the usual mannequin of arithmetic. The proof is predicated on Rasiowa–Sikorski Lemma. The important thing function are performed by the derived notion of a Rasiowa–Sikorski set and the strategy of forcing adjusted to arbitrary first–order languages. This strategy was developed within the papers Czelakowski [4, 5]. The central thought consists in setting up an acceptable countable mannequin AA of Peano arithmetic via a Rasiowa–Sikorski set. This mannequin validates the dual prime conjecture. Since AA is elementarily equal to the usual mannequin, the conjecture follows. Thus the usual mannequin validates the dual primes conjecture. Extra usually, it’s proven that de Polignac’s conjecture has a optimistic answer. The paper employs strategies borrowed from the modern mathematical logic. Such a ’logical’ strategy could also be seen as a helpful addition to the dominant methodology in quantity idea primarily based on mathematical evaluation.
The dialogue at MathOverflow started on October twenty sixth with this remark from “Glycerius”:
It looks like the article “The Twin Primes Conjecture is True within the Commonplace Mannequin of Peano Arithmetic: Purposes of Rasiowa–Sikorski Lemma in Arithmetic (I)” by Janusz Czelakowski revealed in Studia Logica yesterday, claims to have confirmed that the dual prime conjecture holds in the usual mannequin of Peano arithmetic utilizing the strategy of forcing. This looks like a really vital achievement (if the declare just isn’t misguided) however I’m in no way an professional in logic or quantity idea, and due to this fact I’m not certified sufficient to grasp and consider the contents of this paper. So I’d admire others’ inputs on whether or not this declare has benefit.
In an October twenty eighth response, James Hanson (Maryland) claims to establish a central error within the paper:
He goes on to elaborate on this in his remark, which you’ll be able to learn in its entirety here.
Following the publication of Hanson’s remarks, a retraction discover, dated October thirty first, from Studia Logica editor-in-chief Jacek Malinowski appeared on the journal’s website:
Studia Logica is revealed by Springer, however the retraction discover doesn’t seem on the publisher’s pages for the journal, nor are the articles but marked as retracted.
The incident was dropped at my consideration by Eric Schliesser (Amsterdam) on Twitter, the place he famous that it was a victory for post-publication overview, alongside the strains defended by Liam Kofi Bright (LSE) and Remco Heesen (Western Australia, Groningen) (see here).
He additionally noted a strangeness in Malinowski’s retraction discover:
It’s bizarre as a result of he admits to irregularities within the overview course of—with out explaining what they have been. So why assume this authors’ papers are the one ones?
He adds:
I’ve little doubt the apologies are honest (and the duty certainly felt), however apologizing for reputational injury is peculiar. The apology ought to be for the obvious referee shannanigans (favoritism?) and for placing out subpar work.
Have been there “shenanigans”? Catarina Dutilh Novaes (VU Amsterdam) notes:
Line-by-line checking of mathematical proofs is the exception, not the rule. It’s comparatively frequent that errors are discovered post-publication.
But Benedict Eastaugh (Warwick, Munich) says:
It was not laborious to see that this paper had issues, and it didn’t take lengthy for somebody to find a deadly error as soon as it was checked out with a modicum of care. I agree that line-by-line checking is phenomenal, however it might not have been essential on this case.
I’ve requested Malinowski whether or not Czelakowski’s papers had gone via anonymized peer overview however (fairly fairly) he hasn’t gotten again to me but. I’ll replace the submit when he does.
It could be price noting that Studia Logica uses single-anonymized overview, which means the writer identification is thought to the reviewer and the editor. It could even be price noting that Czelakowski is likely one of the associate editors of the journal by which his articles appeared. That raises the possibilty of a possible battle of curiosity that would result in corruption of the peer overview course of, however needn’t if strict measures are adhered to. I’m curious what readers take into consideration that typically.
