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I'm a graduate student at UC Berkeley, studying mathematical logic. I'm especially interested in reverse mathematics and abstract model theory.
2d

comment 
Non Satisfiability of disjuction
This is probably a homework problem, and definitely not appropriate for MO; mathstackexchange would be a better fit. 
Apr 14 
comment 
Universal antiHorn classes?
I suspect that's supposed to allow $\alpha_i$ to be $T$, not just $\alpha_0$? 
Apr 9 
comment 
Elementary book on Matrices
This is a good question, but not for this site; mathstackexchange would be a better fit. 
Apr 5 
comment 
Some NonTrivial Algebraic(Rational) Number
I think you'll be interested in mathoverflow.net/questions/32967/…. In particular, I think Legendre's constant (en.wikipedia.org/wiki/Legendre%27s_constant, mentioned in the first answer) is a pretty good example. 
Apr 5 
revised 
Application of Fraïssé construction in set theory
added 16 characters in body 
Apr 5 
comment 
Application of Fraïssé construction in set theory
Sorry, I didn't realize that  fixed. 
Apr 2 
comment 
Does PA+Con(PA) entail the existence of nonstandard models of PA?
Isn't that the usual statement of Tennenbaum's theorem? 
Mar 23 
awarded  Enlightened 
Mar 23 
awarded  Nice Answer 
Mar 23 
revised 
Does PA+Con(PA) entail the existence of nonstandard models of PA?
added 188 characters in body 
Mar 23 
comment 
Does PA+Con(PA) entail the existence of nonstandard models of PA?
For what it's worth, I disagree with the vote to close. 
Mar 23 
answered  Does PA+Con(PA) entail the existence of nonstandard models of PA? 
Mar 18 
comment 
Surjectivity from union of a set system to the set system
I don't think this works  as I wrote in my comment, I don't think there's an injection $f$ from $\bigcup\mathcal{A}$ to $\mathcal{A}$ satisfying $a\in f(a)$, since 0 and 1 must both be sent to the same place. 
Mar 18 
comment 
Surjectivity from union of a set system to the set system
If you mean $\{\{0, 1\}\}\cup . . .$, I don't think this works  what is the $f$? Otherwise  if we treat numbers as ordinals  0 can't be in $\mathcal{A}$ since $\mathcal{A}$ should consist of nonempty sets only. 
Mar 18 
answered  Surjectivity from union of a set system to the set system 
Mar 17 
awarded  Taxonomist 
Mar 15 
comment 
Surjective (strong) reducibility of Borel equivalence relations
If a Borel equivalence relation $E$ has only countably many equivalence classes, isn't each class Borel? 
Mar 15 
awarded  Nice Answer 
Mar 15 
revised 
Independence of the countable axiom of choice
added 58 characters in body 
Mar 15 
comment 
Independence of the countable axiom of choice
Yes, exactly: without the axiom of choice, it is possible that a countable union of countable sets  in fact, a countable union of finite sets  might not be countable! 