bio  website  math.lsa.umich.edu/~ablass 

location  US  
age  
visits  member for  5 years, 3 months 
seen  12 hours ago  
stats  profile views  12,083 
1d

awarded  Necromancer 
2d

comment 
When did people know that all real polynomials of degree greater than 2 are reducible?
If someone knew long ago that all polynomials over the reals can be factored into polynomials of degree $\leq2$, then all that would be needed to get the fundamental theorem of algebra would be that real quadratics have complex roots. That would be known pretty much immediately after complex numbers are invented. 
2d

comment 
Terminology in combinatorics
The first property says that nonadjacency is a transitive relation (if we count each vertex as nonadjacent to itself). So if you need to invent a name, I'd suggest "cotransitive". 
Jul 31 
comment 
History of unstable formulas
The $n!$ count omits those $n$types that say that two or more of the $n$ elements are equal. (Of course that doesn't affect the point you were making.) 
Jul 30 
comment 
Why only Normed Linear Spaces?
Norms on abelian groups have been used to characterize the free ones: "A Characterization of Free Abelian Groups" by Juris Steprāns, Proceedings of the American Mathematical Society Vol. 93, No. 2 (Feb., 1985), pp. 347349 
Jul 30 
comment 
presentations of subalgebras
Just to make sure I'm understanding the question correctly: The presentation that you seek for the subalgebra $B$ need not use the known $y_1,\dots,y_m$ as its generators but rather can use completely different elements to generate $B$, right? 
Jul 29 
comment 
Recursion, Common Term, Combinatorics
It seems that the $n$th term of your sequence is the largest $k$ such that $2^{k1}$ divides $n$. 
Jul 29 
comment 
The status of 'the consistency of NF relative to ZF'
@AndresCaicedo Do you know whether the "everybody" in your comment includes Bob Solovay? The reasons I ask are that (1) I understand that he paid attention to some of Randall Holmes's earlier work on NF, so he would presumably be interested in the consistency result, and (2) his reputation for careful work leads me to think that, if he were to say that he's studied the proof and thinks it's correct, that would be a huge step toward general acceptance of the proof. 
Jul 24 
comment 
A question about sentences undecidable in Peano's Arithmetic
@DavidRoberts The facts that Con(SOA) is true, that all axioms of SOA are true, that logical inference preserves truth, and that therefore Con(SOA) cannot be refuted in SOA are all provable in the usual foundational system for mathematics, ZFC. (They're also provable in far weaker systems,but I don't think that's needed to answer "How does one get this?") 
Jul 23 
awarded  Nice Answer 
Jul 23 
answered  Are there discontinuities in the large cardinal hierarchy? 
Jul 23 
comment 
A question about sentences undecidable in Peano's Arithmetic
Note that Gödel's paper on the incompleteness theorems is, as indicated in its title, about Principia Mathematica and related systems. Principia Mathematica is considerably stronger than SOA. 
Jul 23 
answered  A question about sentences undecidable in Peano's Arithmetic 
Jul 22 
comment 
Are all polynomial inequalities deducible from the trivial inequality?
The algebraically prime model of the theory of realclosed fields is not the field of rationals (which isn't realclosed) but the intersection of the reals and the algebraic closure of the rationals. 
Jul 20 
comment 
What sort of cardinal number is the LöwenheimSkolem number for secondorder logic?
@JoelDavidHamkins is right. You can't reasonably expect to get models of $T$ that are smaller than $T$. 
Jul 18 
comment 
A question on two modal formulas
One of your comments is sufficiently readable in my browser to address my concern; the $\lozenge$ at the beginning of your first comment was intended to be $\Box$, and then the semantics makes much better sense. The only remaining problem is that the formulas in the question are far too complicated for me to assimilate and say anything about. I hope some experts in modal logic will be able to grasp them and provide useful information. 
Jul 18 
comment 
A question on two modal formulas
I"m somewhat surprised by your comment saying that you use $\lozenge$ for what appears to be a necessity operator ("all worlds $w'$ which are better"), so that, for example, $\lozenge(p\land q)$ is equivalent to $(\lozenge p)\land(\lozenge q)$. Do you use the usual definition of $\Box$ as $\neg\lozenge\neg$, so that it would mean "holds at at least one world which is better"? I would expect hat this inversion of the usual roles of $\lozenge$ and $\Box$ would prevent any close connection between your modal logic and the traditional ones. 
Jul 17 
awarded  Good Answer 
Jul 14 
revised 
Propositional logic without negation
fixed a typo 
Jul 14 
comment 
Why is the settheoretic principle $\diamondsuit$ called $\diamondsuit$?
@AsafKaragila Fortunately, it wasn't quite that bad. The combinatorial square came with a cardinal as a subscript, and The two squares were never in the same formula. (The paper is "Infinitary combinatorics and modal logic" JSL 55 (1990) 761778.) 