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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.

8h
comment What does a Turing machine compute?
@Francois, you're quite right; I should have been more specific. What I meant, was that there is probably not a body of research specifically around varying the i/o interpretations of a given model. (That was what I meant by the last sentence of my first comment.) I should probably clarify that, too, though: some i/o interpretation changes of course have dramatic effects (e.g., unary vs. binary), but Hans' variations fixed some method of representing numbers and varied where on the tape these numbers are to be located, and it was this specific approach that I was saying didn't yield a topic.
12h
comment What does a Turing machine compute?
Basically, anything that looks reasonably like a Turing machine (and some things that don't: mu-recursion, lambda calculus, MRDP theorem, . . .) results in either the same notion of computability, or a strictly weaker notion. I'm not sure of anywhere where it's specifically focused on, but see section 3.2 of Sipser's book "Introduction to the theory of computation." It's obviously hard to make this rigorous, but it's the sort of thing that becomes fairly clear after working with Turing machines and their ilk for a while.
12h
comment What does a Turing machine compute?
I don't really think there's a 'topic' here - there is a well-known robustness phenomenon (pretty much any reasonable notion of interpretation should yield the same notion of computability, or be weaker), so the global picture is the same, and it seems that non-pathological choices of how to interpret outputs will even yield the same complexity classes (assuming these choices are all applied to the same underlying model). So, while in general there's lots of interesting things to say about various Turing-like models of computation, this kind of variation doesn't seem very promising.
13h
accepted When are the congruence lattices nicer?
2d
comment When are the congruence lattices nicer?
Okay, now I follow (I didn't know that those were the only two varieties of distributive lattices). If you post this as an answer, I'll accept it. Thanks!
2d
comment When are the congruence lattices nicer?
I'm sorry, I'm still not following; I think I'm just being slow: given that $V'$ is a lattice of distributive varieties, why can we conclude that $V''$ is either trivial or generated by 2? (Or is it known that these are the only two varieties of distributive lattices? That seems odd.) Also, regardless of this, question 1 still seems potentially interesting.
2d
comment When are the congruence lattices nicer?
I didn't know about that result, that's nice! But I don't see why that implies that ' stabilizes.
2d
asked When are the congruence lattices nicer?
2d
comment Existence of finite nonabelian groups satisfying certain identities
What is the motivation?
Aug
23
comment An algorithm and symbolic manipulation for IF-THEN-ELSE
I'm not really sure what you're asking, but re: question 2 (as far as I understand it) since a statement "If A, then B, else C" can be expressed as "(A and B) or C," why isn't this already captured by standard symbolic logic?
Aug
18
comment A group allowing exactly 7 group topologies
Where can I find proofs of the two claims in your last paragraph (that $G$ must be finite, and that there are such groups admitting $p+3$ topologies for $p$ prime)?
Aug
10
comment Mapping graphs to ordinals
One potential problem is that there are many different ways that one may extend a well-quasi-order to a well-order, so it's not clear that "this ordering" is well-defined. On the other hand, given a well-quasi-ordering we do get a notion of rank, so we can ask what the rank of natural graphs in that wqo is. I don't know what has been done around here - I suspect there is a good deal known - but I would be very interested.
Aug
7
comment Is there any current development of a first order formalization of metamathematics?
I'm confused: in light of Goedel coding, how isn't first-order arithmetic already a "logic of proofs" (and other things besides)? My understanding was that weaker systems, like modal logics of proofs, are fragments of first-order arithmetic, although I could be wrong (theories axiomatizing notions of truth are really really strong, but these aren't quite theories of provability).
Aug
7
comment Examples of research on how people perceive mathematical objects
I think this question is quite interesting, especially in light of the last example, which doesn't just boil down to "we stink at integration" or something similar, but is actually (to me at least) quite neat and surprising. (To be more precise: it doesn't just hinge on a weakness of human mathematics, it hinges on both a human value judgment and a positive aspect of human mathematics, the ability to vaguely identify chaos.)
Aug
4
awarded  Yearling
Aug
2
answered One or two questions about so-called “absolute” set theories
Aug
1
comment Adjunction algebra - is there anything similar to this in abstract algebra?
I've deleted a nonsensical comment. Since your axioms for adjunction algebras include a non-equation, there doesn't seem to be a nice way to build a free algebra: "free on $n$ generators" should mean "epis onto anything $n$-generated," but it's not obvious how to build one (or even if there are any), and of course this is even more true for normal adjunction algebras. On the other hand, a finite adjunction algebra certainly won't be free, so I've left my second comment intact.
Aug
1
comment Adjunction algebra - is there anything similar to this in abstract algebra?
An example of a non-free normal adjunction algebra: consider the set with 2 elements $\{0, 1\}$, with the operation $;$ defined as $0; 1=0$, $0; 0=1$, $1; 1=1$, $a; b=b; a$. This seems to me to yield a normal adjunction algebra, and it is certainly not free.
Jul
28
accepted The word problem of the free left distributive algebra on one generator
Jul
27
comment The word problem of the free left distributive algebra on one generator
I don't have the handbook with me - are these results proved in ZFC alone?