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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 |
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Find examples non compact surface satisfy properties every point is hyperbolic for Gaussian curvature
Is this homework? |
Dec 15 |
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What is a discrete shape
edited tags |
Dec 13 |
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personal relationships
I'm not sure this is appropriate for MO . . . |
Dec 11 |
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Universal graph homomorphisms
Related: mathoverflow.net/questions/130437/… |
Dec 8 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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A question regarding forcing extensions
What does "replace Replacement with Collection in $M[G]$" mean? |
Dec 3 |
awarded | Good Answer |
Dec 1 |
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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 |
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How can we join two points with a small ruler?
@Bogdan, why are you not satisfied with that solution? It seems fine to me. |