Amit Kumar Gupta

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 Name Amit Kumar Gupta Member for 2 years Seen 2 days ago Website Location Berkeley, CA Age 28
Graduate student in set theory at UC Berkeley
 May3 awarded ● Nice Question Apr27 awarded ● Nice Answer Apr20 comment What does a mathematician expect from mathematics education? The question as it stands is unintelligible, and its original intention was purely social commentary. The discussion that's followed is entirely open-ended, highly opinionated, makes no pretense even of there being an attempt to find concrete solutions to concrete problems, and is only vaguely directed at the original post (necessarily so, as the original post doesn't actually make sense in the first place) . How has this not been closed yet? Apr10 comment How much of ZFC do I need to construct this cofinal, order-preserving class function?What's the difference between a cofinal, order-preserving class function, and a class function with cofinal image, assumed to preserve orderings? Apr10 comment How much of ZFC do I need to construct this cofinal, order-preserving class function?For $\Gamma=(L,\leq_L)$ then you get a well-ordering $\mathrm{Ord}\to L$. So in that sense it's "possible." Did you mean for arbitrary $\Gamma$? Apr10 comment How much of ZFC do I need to construct this cofinal, order-preserving class function?It's simpler to just say $\Gamma$ is a well-founded [directed](en.wikipedia.org/wiki/Directed_set) poset with a bottom element and no infinite antichains (making it a [well-quasi-ordering](en.wikipedia.org/wiki/Well-quasi-ordering)). You have a well-ordering $\phi$ due to Choice, there's no need to phrase the claim as a conditional since you're assuming choice to construct $c$ anyways. You can take $\alpha = \mathrm{cof}\Gamma$. Why are you replacing $\phi$? Apr1 comment A “mother of all groups”? What kind of structures have “mother of all”s?Also, your construction of the direct limit of the symmetric groups makes sense in the context of choice, and also gives you a class group which contains an isomorphic copy of every set group. Apr1 comment A “mother of all groups”? What kind of structures have “mother of all”s?Yes, edited.${}$ Apr1 revised A “mother of all groups”? What kind of structures have “mother of all”s?edited body Apr1 revised A “mother of all groups”? What kind of structures have “mother of all”s?added 1507 characters in body Apr1 answered A “mother of all groups”? What kind of structures have “mother of all”s? Jan29 comment Can FPA really prove its consistency?What do you mean one cannot prove there exists $n$ such that $one(n)$? (PA2) with $n=0$, together with (PA1), gives precisely $\exists m \mathrm{one}(m)$. Jan6 comment Theorems about endofunctions and closures(math.stackexchange.com) would be a better venue for this question, as mathoverflow is designed for research-level mathematics. Dec26 comment a measurable cardinal & a real-valued measurable cardinal in the same model?The question you're asking is equivalent to asking whether ZFC is inconsistent. Dec26 accepted Is there a name for the smallest ordinal $\alpha$ such that $X \subseteq \alpha$ Dec26 answered Is there a name for the smallest ordinal $\alpha$ such that $X \subseteq \alpha$