Coincidentally, a paper based on Yudkowsky and Herreshoff's paper has appeared a few days ago on the arXiv. It's Paradoxes of rational agency and formal systems that verify their own soundness by Nik Weaver. Here's the abstract:
We consider extensions of Peano arithmetic which include an assertibility predicate. Any such system which is arithmetically sound effectively verifies its own soundness. This leads to the resolution of a range of paradoxes involving rational agents who are licensed to act under precisely defined conditions.
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= f037147d6e6c911a85753b9abdedda8d)
"whose only factors" -- that's where you are hiding the negation
("only" = "there is no other")
Not necessarily: see mathnerd314's comment below (or above). In fact, in “there is no other”, there is a double negation (the second being in “other”, which hides “not equal to”), which can be eliminated.