27,786 reputation
375159
bio website dorais.org
location Hanover, NH
age
visits member for 4 years, 8 months
seen 13 mins ago

I like math and a few other things...


3h
comment If questions are formalized as ideals of a boolean algebra, what kind of algebra of questions appears from Stone representation theorem?
This looks very similar to what is often known as "Medvedev's logic of finite problems" in the context of intermediate logics.
1d
revised The (un)decidability of Robinson-Arithmetic-without-Multiplication?
Added the original axiom 1 since it has been edited in the question.
1d
accepted The definition of < in Robinson's Q
1d
comment The definition of < in Robinson's Q
Thanks Emil! That makes a lot of sense. I guess everybody is just following the original definition.
2d
comment The definition of < in Robinson's Q
@ChristianRemling: I noticed that too but according to Google books, Burgess actually suggests defining $x \lt y$ as $\exists z(z' + x = y)$. I haven't read the book though, so I'm not sure about the context.
2d
revised The definition of < in Robinson's Q
typos
2d
revised The definition of < in Robinson's Q
edited tags
2d
asked The definition of < in Robinson's Q
Jul
21
revised Mixed integer programming formulation for Ising model
edited tags
Jul
21
revised proof for unsolved problem
edited tags
Jul
20
comment Alternative definition of a category
@Bob: I recommend getting a copy of that book, it's a good read. The book is about categories and allegories. Their approach to categories (and allegories) is essentially object-free.
Jul
20
comment Alternative definition of a category
See also Categories and Allegories by Freyd and Scedrov.
Jul
17
comment Embeddings of forcing notions - preserve properness?
An interesting counterexample to $(D4)\Rightarrow(D3)$ is due to Zapletal in On the existence of a $\sigma$-closed dense subset MR2741884. Zapletal shows that it is consistent to have two dense subsets $P$ and $Q$ of some poset such that $P$ is $\sigma$-closed but $Q$ has no $\sigma$-closed dense subset. It's an open question whether the existence of such $P$ and $Q$ is provable in ZFC.
Jul
16
revised Is it compatible with ZF to assume that every amenable discrete group is finite?
fixed omegas
Jul
16
answered Is it compatible with ZF to assume that every amenable discrete group is finite?
Jul
16
comment Is quasivariety generated by all perfect graphs finitely axiomatizable?
@AndrásSalamon: Since the $\sigma_k$ are a complete axiomatization, they prove the purported finite axiomatization. Such a proof uses only finitely many of the $\sigma_k$, which together form a complete axiomatization.
Jul
15
comment If there are two primes at an even distance $k$ is there another disjoint pair of primes also at distance $k$?
No, I was just happy you addressed that flimsy interpretation in your answer!
Jul
15
comment If there are two primes at an even distance $k$ is there another disjoint pair of primes also at distance $k$?
The question is perhaps poorly worded but as it stands now it only asks that: for every even $k$, there is not exactly one pair of primes at distance $k$ from each other. Though unusual, I find that question interesting too.
Jul
14
revised Is every set class generic over a given inner model?
for searching
Jul
8
comment Does V=L imply transitive containment over, say, Z?
Most formulations of $V = L$ make transitive containment redundant. Whether you use the Gödel $L_\alpha$, Jensen $J_\alpha$ or other hierarchies, these are transitive by design so formal statements for V = L, like $\forall x \exists \alpha (Ord(\alpha) \land x \in L_\alpha)$, immediately imply transitive containment. Transitive closure is a bit tricky but it often follows too.