A. Kiselev says that he proved that: ZF+Exist k. k is weakly inaccessible cardinal, is inconsistent. http://lanl.arxiv.org/find/all/1/ti:+AND+Inaccessibility+Subinaccessibility/0/1/0/all/0/1 http://arxiv.org/abs/1010.1956 http://arxiv.org/abs/1011.1447. Is the arxiv.org web site a reputable math reference? Are the papers there reviewed, the proof know to be correct? Does Kiselev's proof end the notion of inaccessible cardinals? ----
No; it's mainly a pre-print server. No, not at all. This is all mentioned in the "About the arXiv" and "arXiv primer" links you can access by clicking on the "Help" link in the top right. The closest it comes is: "Submissions are reviewed by expert moderators to verify that they are topical and refereeable scientific contributions that follow accepted standards of scholarly communication (as exemplified by conventional journal articles)." Note: referee**ABLE**, not referee**D**. In short: they should look like something a journal would send out for being refereed, and not an obvious crank work. No checking for actual accuracy/correctness is done, and some sections of the arXiv have a fair amount of crank papers anyway (e.g., the General Mathematics section). Presumably, only if it is ever vetted and verified; certainly not merely by being put in the arXiv.
