# Chuck

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 Apr14 awarded Yearling Apr10 awarded Good Answer Jan11 comment Clarification of a remark of J. Steel on the independence of Goldbach from ZFC@alancalvitti No because the Euclidean axioms are not $\Pi^0_1$-sound. Jan11 accepted Clarification of a remark of J. Steel on the independence of Goldbach from ZFC Jan10 comment Clarification of a remark of J. Steel on the independence of Goldbach from ZFCBy the way, I am not the one who downvoted Jan10 comment Clarification of a remark of J. Steel on the independence of Goldbach from ZFCThanks a lot for the super quick response, but I'm afraid I don't understand. What is M[G]? What are we assuming about M? I'm sorry but I don't see how Steele's remark follows from this at all...Is the idea this: Let's start with any model M of ZFC and then force a model 'M[G]' in which $\phi$ is true (or false), then $\phi$ is true or false in the model we started with? But how does that ensure it is provable in PA? Why couldn't it turn out to be undecidable? Could I convince you to expand on your answer? Jan10 asked Clarification of a remark of J. Steel on the independence of Goldbach from ZFC Aug13 comment Where else has Proposition B1.3.17 in the Elephant been proved?@QiaochuYuan I know cross-posting is discouraged, but would it be bad form if I re-posted this on mathoverflow? Aug13 comment Where else has Proposition B1.3.17 in the Elephant been proved?@ZhenLin Yes I do have Streicher's notes which are generally very helpful. He proves this result for the specific property of local smallness (Lemma 13.3) but not the much more general result that Johnstone proves. Of course reading Streicher more carefully, he seems to imply (top of pg. 47, just before the proof of 13.3) that Benabou also only proved such results for specific properties. So it seems Johnstone was the first to present this result in this general form - and therefore that this is the only proof that we have... Aug12 comment What is the formula for this exponentially growing “stairs”?Do you need all the points (i.e. the where the vertical meets the horizontal) of each step to lie on a straight line? Aug11 comment Where else has Proposition B1.3.17 in the Elephant been proved?@Qiaochu Haha, you are right - I meant the former, i.e. so condensed as to make it difficult to understand. Aug11 asked Where else has Proposition B1.3.17 in the Elephant been proved? Aug7 comment Why is the landing footprint an ellipse?Yes, thanks, I appreciate your answer but that's exactly what I wrote in the question - I was asking whether there's anything more than that Aug6 asked Why is the landing footprint an ellipse? May4 comment How to get a geometric morphism out of a section? (And general pedagogy on classifying toposes)Thanks for this answer. I don't understand what version of the SAFT you are using there (which I associate with the existence of a left adjoint)? I'm assuming what you have in mind is the theorem that says that a functor between Grothendieck toposes has a right adjoint iff it preserves colimits. However we cannot know that the toposes in question here are Grothendieck. Maybe I'm missing something.... May2 awarded Nice Answer May2 comment In the history of mathematics, has there ever been a mistake?@Zarrax I suspected he must've had some serious formal training in math, but never knew that - edited accordingly May2 revised In the history of mathematics, has there ever been a mistake?added 19 characters in body May2 comment In the history of mathematics, has there ever been a mistake?Oh I didn't notice it had been given there - apologies, that one's a better answer.... May2 answered In the history of mathematics, has there ever been a mistake?