bio | website | math.berkeley.edu/~sramesh |
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location | Berkeley, CA | |
age | 29 | |
visits | member for | 4 years, 7 months |
seen | 10 hours ago | |
stats | profile views | 3,536 |
I am 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.
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). |
Oct 21 |
asked | Properly “transfinitely” Euclidean domains |
Oct 4 |
answered | wellfounded sets and predecessors |
Oct 3 |
comment |
“Mathematics talk” for five year olds
Naive question: what is the sense in which these final tessellations live in FOUR-space? |
Sep 23 |
comment |
Is it possible to have t triangles in some graph on n vertices?
It's not clear to me that {1, 2, ..., n} is contained in $T_n$. How do I get 2 or 3 triangles with just 3 vertices? |
Sep 19 |
comment |
Reductio ad absurdum or the contrapositive?
("If a proof if" should be "If a proof of", of course. I am too lazy to delete the comment and retype the whole thing just to fix it) |
Sep 19 |
comment |
Reductio ad absurdum or the contrapositive?
If a proof if $p$ implies $q$ by contrapositive (establishing $\neg q$ implies $\neg p$) is useful because one learns intermediately that ($\neg r_1$ implies $q$), ($\neg r_2$ implies $q$), etc., then a proof of $p$ implies $q$ by contradiction (establishing $\neg (p \wedge \neg q)$) is useful because one learns intermediately ($p \wedge \neg r_1$ implies $q$), ($p \wedge \neg r_2$ implies $q$), etc. |
Sep 17 |
comment |
Groupoid interpretation of type theory
Does "groupoid" really need a diaeresis over the "i"? |
Sep 2 |
comment |
Intuitionistic consistency of surjection from naturals to reals
(Also, returning to the dependent choice-based argument against a surjection from N to R, I'm not sure this argument would work when R = MacNeille reals, since it depends on the dichotomy "Either $a_n > (3u + 2v)/5$ or $a_n < (2u + 3v)/5$", which seems an example of precisely the sort of thing which isn't guaranteed for general MacNeille reals) |
Sep 1 |
comment |
Intuitionistic consistency of surjection from naturals to reals
Well, that's the embedding I'm thinking of too, but it's not obvious to me that $1 \in e(q) \Rightarrow q$. After all, the (only classically injective) lattice homomorphism from $\Omega$ to $\Omega_{\neg \neg}$ is also given by $e(p) = \sup \{1 | p \}$ (as is any suplattice-with-top morphism on the domain $\Omega$). |