bio  website  dorais.org 

location  Hanover, NH  
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visits  member for  4 years, 5 months 
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I like math and a few other things...
1d

comment 
Can we construct cohomolgy theory on noetherian separated schemes without Axiom of Choice?
David, there is a general problem with stalks without AC in that there might not be enough of them to ensure things like "surjective" = "surjective on stalks" make sense (depending on how things are set up). However, when suitably formulated, noetherianness should ensure enough stalks to make your assumptions work. 
Apr 17 
revised 
Suslin lines hereditarily Lindelof
edited tags 
Apr 15 
comment 
A question about small sets of reals
To complement the question, the recent paper by Goldstern, Kellner, Shelah, Wohofsky establishing the relative consistency of BC+dBC is here and on the arxiv. Also, Goldstern's overview of the proof is on the arxiv. 
Apr 12 
revised 
Showing that it is a matroid with axioms
edited tags 
Apr 12 
comment 
Is there an intuitionistic generalized boolean algebra (of Stone)?
The generalized Boolean algebras that the OP is talking about always have a bottom element. The difference is that they only have a relative complement operation $x  y$ rather than an absolute complement $x$. Thus they always have a bottom $0 = x  x$ and they are Boolean algebras precisely when they have a top $1$, in which case the complement of $x$ is the relative complement $1x$. 
Apr 11 
comment 
Is there an intuitionistic generalized boolean algebra (of Stone)?
How about a Boolean ring without identity? en.wikipedia.org/wiki/Boolean_ring 
Apr 8 
comment 
$\aleph$ looks like $\mathbb N$?
The $\aleph$ notation appears in Cantor's Contributions to the Founding of the Theory of Transfinite Numbers. As far as I can tell, N wasn't used there to denote the set of natural numbers. This suggests that the answer is 'no'. 
Apr 7 
comment 
Subposets of small DushnikMiller dimension
Wonderful! Thank you both! 
Apr 4 
reviewed  Approve suggested edit on Intuition on Lindeberg condition 
Apr 2 
awarded  axiomofchoice 
Apr 1 
comment 
Is every Heyting algebra the Lindenbaum algebra of an intuitionistic first order theory?
@godelian: There is an $H$valued model that separates all equivalence classes. 
Apr 1 
comment 
Is every Heyting algebra the Lindenbaum algebra of an intuitionistic first order theory?
@godelian: In the classical case, that the theory is satisfiable is equivalent to BPI, but no choice is needed to see that the theory is consistent. 
Apr 1 
answered  Is every Heyting algebra the Lindenbaum algebra of an intuitionistic first order theory? 
Mar 31 
revised 
On a modal correspondence
deleted 27 characters in body 
Mar 29 
comment 
$n$th order arithmetic with predicates for orders
One subtlety (that fortunately doesn't affect arithmetic theories much) are empty domains and their effect on the behavior of the existential quantifiers. In the usual interpretation of multisorted logic, $\exists x^1(x^1 =_1 x^1) \lor \cdots \lor \exists x^n(x^n =_n x^n)$ is not a tautology but $\exists x(x = x)$ is usually a tautology in classical singlesorted firstorder logic. It's perhaps best to use free logic or similar when encoding using the singlesorted version, or to relax $\forall x(Z_1(x) \lor \cdots \lor Z_n(x))$ a bit to allow for all domains to be empty. 
Mar 20 
awarded  Nice Answer 
Mar 19 
comment 
Order homomorphism functions on $\omega_1$
@MonroeEskew: The OP had originally written decreasing instead of regressive. Noah was just a bit too nonhappy when he wrote his comment. 
Mar 19 
comment 
Order homomorphism functions on $\omega_1$
Since there are regressive functions with unbounded range but every function in $K$ has bounded range, you can't always have $f \leq h(f)$. (Assuming regressive is what you meant.) 
Mar 19 
comment 
Order homomorphism functions on $\omega_1$
@NoahS: That doesn't satisfy $f \leq h(f)$. 
Mar 19 
revised 
Order homomorphism functions on $\omega_1$
added 54 characters in body; edited tags 