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 Yearling
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Jun
22
revised What's correspondence between the model theoric and the set theoric kernel of homomorphism?
clearify
Jun
22
asked What's correspondence between the model theoric and the set theoric kernel of homomorphism?
Jun
5
awarded  Yearling
May
20
accepted Which logic is stronger? SOL or $\frak{L}_{\infty,\infty}$?
May
8
awarded  Caucus
Apr
27
revised Which logic is stronger? SOL or $\frak{L}_{\infty,\infty}$?
clearify
Apr
27
asked Which logic is stronger? SOL or $\frak{L}_{\infty,\infty}$?
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
asked Can we conclude that $|\prod_{\xi \in Ord, \xi=1}^{\xi<\alpha}\xi|=2^{|\alpha|}$ for all infinite ordinal $\alpha$ in $\mathsf{ZFC}$?
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
accepted Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
Apr
16
revised Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
correctify
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
revised Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
fix
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
revised Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC?
fix
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.