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location Unknow Galaxy
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visits member for 2 years, 5 months
seen Dec 20 '13 at 18:33

A student in Philosophy but also curious in many fields.


I don't know,

But I want to know.


Aug
4
comment Is there any countable ordinal number which has a member undefinable?
Helpful, thank you.
Jul
16
comment Is there any countable ordinal number which has a member undefinable?
@CarlMummert I was trying to understand you. Would you please show me more detail? Do these models of ZFC, which every set is definable over the model, themselves may have uncountable(outside) many subsets? Or the cardinalities of their powersets are all at most countable(outside), but some of which are uncountable(inside)? Besides, what about $(V,<)$?
Jul
16
comment Is there any countable ordinal number which has a member undefinable?
It's nice for me, thank you.
Jul
16
comment Is there any countable ordinal number which has a member undefinable?
@CarlMummert "There are models of ZFC in which every set is definable over the model". Did you mean definable with parameters, or just definable(without parameters)?
Jul
3
comment What's correspondence between the model theoric and the set theoric kernel of homomorphism?
Okay, it is right now.
Jul
2
comment What's correspondence between the model theoric and the set theoric kernel of homomorphism?
Thank you for answering and sorry for late commenting as I'm in traveling yesterday. I have a question: do you mean $ker(h)$ the set-theoric kernel if $h$? If so, then $ker(Id_{\mathfrak{A}})=Id_{\mathfrak{A}} \ne \emptyset$ whenever $\mathfrak{A}$ is not empty, but $Id_{\mathfrak{A}}$ is an automorphism, hence an embedding. Thus $\ker_m(Id_{\mathfrak{A}})=diag(\mathfrak{A})$ but $ker(Id_{\mathfrak{A}}) \ne \emptyset$ in cases $\mathfrak{A}$ is not empty...
Jun
23
comment What's correspondence between the model theoric and the set theoric kernel of homomorphism?
@kahen Thank you for your suggestion.
Jun
23
comment What's correspondence between the model theoric and the set theoric kernel of homomorphism?
@tomasz Okay, I have clarified my post.
Apr
16
comment Can we conclude that $|\prod_{\xi \in Ord, \xi=1}^{\xi<\alpha}\xi|=2^{|\alpha|}$ for all infinite ordinal $\alpha$ in $\mathsf{ZFC}$?
@Apostolos Thank you, that's all right.
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
Thank you for your suggestion.
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
Thank you very much. Besides, a little tip: when $\alpha=\beta+1$ then $\Gamma(\aleph_\alpha)$ should be $2^{\aleph_0}\aleph_{\beta}^{|\beta|}$.
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
I'm sorry that I have made another error: this product is the cardinal product of all positive cardinals smaller than $\aleph_\alpha$ whereas in the lemma 1 I had considered it as the cardinal product of all positive ordinals smaller than $\aleph_\alpha$.
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
I'm sorry about that...
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
@AsafKaragila Sorry, in that time I have mistook the definition of beth numbers (mistook that $2^{\aleph_\alpha}=\beth_{\alpha+1}$).
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
Thank you, it's amazing.
Apr
16
comment Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
@CliveNewstead Thanks, I'm going to fix it.
Apr
12
comment Entropy: Is $H(X_{1},X_{2}) = H(X_{1})$ true?
You are welcome.
Apr
10
comment Given a relation $R$, is it reflexive? Symmetric? Transitive?
$R$ is not transitive. Let $a=6,b=15,c=35$, you can easily check them.
Apr
7
comment Difference between “Live” and “Define”
@suissidle The word let sometimes used as define but informally. What's more, it sometimes used as assign, e.g. let $x=0,y=1$.
Apr
6
comment What's the remainder of a natual number divided by lcm(m,n)?
Thank you, I have improved my question.