2,443 reputation
1527
bio website math.berkeley.edu/~sramesh
location Berkeley, CA
age 30
visits member for 5 years, 5 months
seen 18 hours ago

I was a graduate student in the Logic program at Berkeley, broadly interested in categorical logic and foundations of mathematics, as well as in applications of category theory to the semantics of programming languages. I work for Google now.


Jun
25
awarded  Pundit
May
24
comment Avoiding reflexive paradox in set theory
Richard, you are coming now quite close to a principle like "Sets are given by well-founded comprehension"; this is the spirit behind ZF, and once you have that, the rest of its axioms are not far behind [you'll find that the existence of infinite sets, powersets, etc., are not automatically assured, and you may want to assure them].
Mar
29
awarded  Nice Answer
Mar
1
awarded  Popular Question
Feb
10
awarded  Nice Answer
Feb
8
awarded  Yearling
Dec
1
comment Application of polynomials with non-negative coefficients
Surely, the thing to do is to use q = p(1) + 1 rather than q = p(1), so as not to have to treat the case p(q) = q^n on an ad hoc basis.
Nov
19
revised Proof without words for surface area of a sphere
added 126 characters in body
Nov
19
revised Proof without words for surface area of a sphere
edited body
Nov
19
revised Proof without words for surface area of a sphere
added 43 characters in body
Nov
19
answered Proof without words for surface area of a sphere
Nov
18
comment There are two points on the Earth's surface that … ?
What does "separated by the same geodesic distance" mean for two points?
Nov
17
comment Tarski's Theorem and Gödel's Second Incompleteness Theorem
Well, one caveat: One needs that Tarski's result is constructive enough that we have not just "For every T, for every model, there is a G such that...", but in fact "For every T, there is a G such that for every model...". But, basically, were Tarski's result phrased as strongly as its proof actually warranted, it would give us everything.
Nov
17
comment Tarski's Theorem and Gödel's Second Incompleteness Theorem
I've modified the word of the second paragraph to alleviate this concern. The second incompleteness theorem follows from the simultaneous "external" and "internal" truth of Tarski's theorem (by which I mean, the fact that Tarski's theorem is both true and provable (or, just as well, true inside every model)).
Nov
17
revised Tarski's Theorem and Gödel's Second Incompleteness Theorem
added 56 characters in body
Nov
17
revised Tarski's Theorem and Gödel's Second Incompleteness Theorem
added 67 characters in body; added 32 characters in body
Nov
17
answered Tarski's Theorem and Gödel's Second Incompleteness Theorem
Nov
2
comment Entailment and implication
It's also worth noting that the trivial topos, like all toposes, internally considers itself to be non-trivial. It just happens to also consider itself to be trivial...
Nov
2
comment Entailment and implication
In the internal logic of the trivial topos, "there is no rational square root of two" is true. It's just that "there is a rational square root of two" is also true. The internal logic of the trivial topos happens to validate all statements; that's what makes it so trivial. But it also means it doesn't harm anything, or make any difference to the model-theoretically valid statements, to consider it a legitimate model.
Oct
21
comment Properly “transfinitely” Euclidean domains
I don't think the omnific integers can admit an ordinal-valued (as opposed to omnific integer-valued) Euclidean function; an ordinal-valued Euclidean function should still lead to being a unique factorization domain, in the usual way, but the omnific integers lack unique factorization (e.g., 2, 3, 5, 7, ..., all remain prime, but $\omega$ is divisible by all infinitely many of them).