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I'm a graduate student at UC Berkeley, studying mathematical logic. I'm especially interested in reverse mathematics and abstract model theory.

Dec
16
comment Find examples non compact surface satisfy properties every point is hyperbolic for Gaussian curvature
Is this homework?
Dec
15
revised What is a discrete shape
edited tags
Dec
13
comment personal relationships
I'm not sure this is appropriate for MO . . .
Dec
11
comment Universal graph homomorphisms
Related: mathoverflow.net/questions/130437/…
Dec
8
comment Generalizations of the Four-Color theorem
Is it known whether this is the same as the chromatic number of maps whose regions are convex subsets of $\mathbb{R}^d$?
Dec
6
comment Can there be ordinals larger than those contained in Ord, and if so, can they be used to extend the constructible universe $L$?
Ah! This makes more sense. Presumably other people will have more to say about it, but let me just direct you to a beautiful theorem of Barwise that says that any model of $ZFC$ has an end extension which is a model of $V=L$. So in principal, any model arises as part of the constructible universe of another model. Of course, the models Barwise's theorem produces are not well-founded, so their "ordinals" aren't, really; but it's still interesting. You might also find this question of mine relevant: mathoverflow.net/questions/171703/…
Dec
6
comment Can there be ordinals larger than those contained in Ord, and if so, can they be used to extend the constructible universe $L$?
I'll try one last time: What do you mean by "applies Shoenfield's principle to $L$"? Are you asking the following: "Suppose $V\models ZFC+V=L$, $\kappa\in Ord(V)$, and $V_\kappa\models ZFC+V=L$; then what are some ways $V$ and $V_\kappa$ can be different?" Or are you asking, "Given a model $M$ of $ZFC+V=L$, is there another model $N$ such that $M=L_\alpha^N$ for some $\alpha\in N$?" Or what? I'm not being deliberately slow, I honestly don't know precisely what you are asking; and with this sort of question, precision is really important.
Dec
6
comment Can there be ordinals larger than those contained in Ord, and if so, can they be used to extend the constructible universe $L$?
That's what I don't get, really - what do you mean "if Shoenfield's principle holds?" It's not written as a precise mathematical statement, so I'm not sure how I'd distinguish between a structure in which it was true and a structure in which it wasn't. There are a few precise questions here I could imagine being related - "what happens if you try to continue the $L$-construction through class-well-orderings?" is one - but I really don't know what you are asking. As for $M[H]$ (a la Blass), that's just an initial segment of a $ZF$ model; is that all it takes to satisfy Shoenfield's principle?
Dec
6
comment Can there be ordinals larger than those contained in Ord, and if so, can they be used to extend the constructible universe $L$?
I don't really understand the question - could you clarify what you are asking?
Dec
5
comment Formal languages with non-unique interpretations of terms
Yes, equality was not always assumed to be a logical notion - for instance, if I recall correctly Robinson's book "Complete Theories" is about first-order logic without equality.
Dec
4
answered Formal languages with non-unique interpretations of terms
Dec
4
comment NP-completeness of Ising model
Yes, which is why I wrote that "saying that something is $NP$-complete . . . does imply that the problem is in $NP$." As to taking exponential time, $EXPTIME$ is not known to be equal to $NP$; in fact, "$EXPTIME=NP$" is known to imply "$P\not=NP$." As a matter of fact, it is generally conjectured that $EXPTIME$ is strictly larger than $NP$. So knowing that something is $NP$-complete in no way implies that it takes exponential time to solve deterministically.
Dec
4
comment NP-completeness of Ising model
This is a good question, but not for this site. Short response: saying that something is $NP$-complete is not the same as saying that it takes exponential time to solve, and does imply that the problem is in $NP$.
Dec
3
comment A question regarding forcing extensions
The answer's rather long, but the short version is: I do think of every set as "potentially countable," so insofar as I imagine a "real" universe of sets (which I usually don't), it's one with that property. It's also a very useful (for me) picture to have in order to think up counterexamples for things. Also, I'm interested in how ideas around countable objects (ex: computable structure theory) can be "lifted up" to uncountable settings, and I find that such a picture of the universe helps me get the right intuition for things.
Dec
3
comment A question regarding forcing extensions
Not really, since "the reals are uncountable" would still be true in it - it's just that the reals would form a proper class instead of a set. (That's not to say that this kind of model wouldn't appeal to a certain philosophical stance - personally, I find it very attractive.)
Dec
3
comment A question regarding forcing extensions
I guess I was confused by "how would that effect $M[G]$," since that implies some sort of change in $M[G]$ itself - I was expecting to see "does collection remain?" instead.
Dec
3
comment A question regarding forcing extensions
What does "replace Replacement with Collection in $M[G]$" mean?
Dec
3
awarded  Good Answer
Dec
1
comment Prove existence of different programs printing each other code
This is a neat problem, but I've seen this as a homework assignment in introductory computability theory courses, so I'm not sure this is appropriate for MO. (Still, I haven't voted to close.)
Dec
1
comment How can we join two points with a small ruler?
@Bogdan, why are you not satisfied with that solution? It seems fine to me.