3,357 reputation
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bio website cwru.edu/artsci/phil/…
location Case Western Reserve University
age 63
visits member for 2 years, 8 months
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Dec
13
comment Widely accepted mathematical results that were later shown wrong?
But this proof was immediately rejected. See mathpages.com/home/kmath447.htm In short in 1847 Lame' announced his proof of Fermat's Last Theorem. Liouville immediately took the floor to criticize the crucial point. It transpired that Kummer had already (three years before) published a paper showing the failure of unique factorization in some of the relevant fields.
Dec
12
comment Higher order arithmetic and fragments of ZFC
@FrançoisG.Dorais More than that I believe you need the control over cardinality that constructibility gives, just as Simpson does for the case of 2nd order arithmetic and ZF[0] in SOSOA. And this is complicated in higher orders because to put it naively $n+2$ order arithmetic tells you what (not necessarily constructible) $\beth_n$ is but when $n>0$ this tells you nothing about how far from constructible $\beth_n$ that may be.
Dec
12
comment Higher order arithmetic and fragments of ZFC
This is the right technology, but I do not think it will give replacement without considerations of constructibility and hereditary constructible countability and its analogues to make each higher order correspond to one higher cardinal.
Dec
11
accepted Consistency of the collection axiom scheme compared to replacement
Dec
11
asked Consistency of the collection axiom scheme compared to replacement
Dec
11
comment Higher order arithmetic and fragments of ZFC
@JoelDavidHamkins Actually Zbierski is not explicit about those issues, and following the tradition of proof theory his proofs are telegraphic and rest heavily on what it is "easy to see." So it is not easy to see exactly what axioms he has in mind for ZFC. His arithmetic axiom scheme of choice says wherever a formula $F(x,y)$ relates every order $n$ set to at least one order $n+1$ set then there is some single order $n+1$ set $z$ collecting codes for order $n$ pairs such that each $x$ is $F$-related to the set $z^{(x)}$ of all $u$ such that code for $\langle x,u\rangle$ is in $z$.
Dec
11
asked Higher order arithmetic and fragments of ZFC
Dec
11
accepted Are there known ways to posit definable global choice in ZF without positing V=L?
Dec
10
revised Are there known ways to posit definable global choice in ZF without positing V=L?
Incorporate insight from the comments.
Dec
10
asked Are there known ways to posit definable global choice in ZF without positing V=L?
Nov
19
comment Robotics, Cryptography, and Genetics applications of Grothendieck's work?
It is fair to ask the question, since the NYT said this. But you are right to be skeptical. There are no major applications in these field though it would be foolhardy to say no one ever claimed to see connections.
Nov
19
awarded  Notable Question
Nov
18
comment When was Bounded Zermelo set theory first formulated?
And that is why Jensen would later take this route for consistency of NFU.
Nov
18
accepted When was Bounded Zermelo set theory first formulated?
Nov
18
answered When was Bounded Zermelo set theory first formulated?
Nov
17
asked When was Bounded Zermelo set theory first formulated?
Sep
25
accepted Reverse mathematics of meromorphic functions on Riemann surfaces
Sep
25
awarded  Nice Question
Jul
7
comment Does V=L imply transitive containment over, say, Z?
@EmilJeřábek Sure, or in other words I want to know if adding V=L to MAC makes Tco redundant.
Jul
6
comment Does V=L imply transitive containment over, say, Z?
Thank you. But I am asking when V is closed under transitive closure, not just when there is inner model with transitive closures.