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bio website dorais.org
location Hanover, NH
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visits member for 5 years, 4 months
seen 3 hours ago

I like math and a few other things...


Mar
24
revised Normalizing Entries In Defining Random Matrices (Wigner Matrix)
typo
Mar
24
revised Analytical value for the first eigenvalue of a certain spherical triangle
typo
Mar
13
comment Is there a version of Miller forcing “guided by” an ultrafilter?
@ToddEisworth No, this would be true if "minimal degree" meant "minimal real degree", as it often does, but Miller and Groszek consider minimal degrees in the general sense: if $X \in M\setminus M[G]$ then $G \in M[X]$.
Mar
10
awarded  Popular Question
Feb
18
revised The difference between an étale finite group scheme and a finite group
added accents
Feb
13
comment The groupoid of algebraic expressions and proofs
@ZhenLin: The identity types lead to an $\infty$-groupoid structure. To get a plain groupoid, one needs to truncate...
Feb
7
comment Ordinary mathematics in Chang's model
Yes, that's what I'm looking for! Where is the Hilbert space from? How did it land in the Chang model?
Feb
7
comment Ordinary mathematics in Chang's model
Every model of ZF is closed under internally constructed countable sequences. I'm wondering why you need external countable sequences for (especially since you're assuming DC).
Feb
7
comment Ordinary mathematics in Chang's model
Welcome to MO! Do you ever need countable sequences built outside the model? If so, it would be interesting to know where (even if the use is not strictly necessary, in fact it could be even more interesting if it's not actually necessary).
Feb
7
comment Ordinary mathematics in Chang's model
@Nik, for the analogous result for $L(\mathbb{R})$ you don't need quite so much (just one limit of Woodins, if I recall correctly). There is much more literature on $L(\mathbb{R})$ than there is on $L(\mathrm{Ord}^\omega)$. This is true at least in the literal sense, though one would expect many of the $L(\mathbb{R})$ results to lift to $L(\mathrm{Ord}^\omega)$ after some adjustments...
Feb
6
comment What do you do if you believe a problem is undecidable?
@Pace "Is there any literature on making rings into Turing machines?" That's the wrong way around, you typically want to interpret Turing machines into ring structures.
Feb
6
comment Ordinary mathematics in Chang's model
Interesting. Is there any reason why Kornell uses Chang's model $L(\mathrm{Ord}^\omega)$ instead of the "more popular" $L(\mathbb{R})$? At some point he states that his results work in $ZF + AC_{ae} + DC + LM + BP + PSP$, which is much weaker than $L(\mathrm{Ord}^\omega) \models AD^+ + DC + AC_{\mathbb{R}}$. That leads me to think that Kornell might be happy with $L(\mathbb{R})$. (By the way, the axiom of choice can hold in Chang's model but it doesn't have to, and the axiom of choice is excluded in Chang's model by some large cardinal hypotheses.)
Feb
4
answered Is there a nontrivial maximally recursive function?
Jan
27
revised Notion of strongness in cut rule
latexified
Jan
26
comment Adding a real with infinite conditions
@Asaf The generalized Cohen forcing and generalized Silver forcing were introduced by Serge Grigorieff Combinatorics on ideals and forcing, Ann. Math. Logic 3 (1971), 363-394; MR0297560.
Jan
25
comment Recent trends in effective analysis
@JasonRute This is a pretty good answer. Maybe there are a few more details to add, but it's a really good summary of the current state of affairs. Why not post it as an answer?
Jan
23
comment On whether a formula of KP is $\Pi_3$
Do you mean $\Pi^0_3$ and $\Delta^0_1$?
Jan
21
comment Krein Milman theorem without the axiom of choice
There is a quantifier error in the "assertion". The assertion (*) in the paper has an implicit universal quantifier.
Jan
20
revised Does k(X) have a k-basis for every set X, without AC?
fixed small typos
Jan
20
awarded  Good Answer