634 reputation
628
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location Unknow Galaxy
age
visits member for 2 years, 6 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.


Apr
4
answered Why don't we study algebraic objects with more than two operations?
Apr
4
accepted Are there rules in the useage of prepositions in Math?
Mar
30
revised Are there rules in the useage of prepositions in Math?
fix
Mar
30
comment Are there rules in the useage of prepositions in Math?
@TaraB I think that the 'form word' I expressed is 'syntactic expletive', but in precisely in this post they are indeed prepositions.
Mar
30
revised Are there rules in the useage of prepositions in Math?
fix
Mar
30
comment Are there rules in the useage of prepositions in Math?
Yes, you are right.
Mar
30
asked Are there rules in the useage of prepositions in Math?
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Okay, let $\mathbf 1=Cn(\emptyset)$ is well. Both $\mathfrak F(\mathcal L)$ and $\mathfrak F(\mathcal L)/ \Leftrightarrow$ can be complete lattice.
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
added 4 characters in body
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
rolled back to a previous revision
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Unfortunately, it isn't, e.g. $\{p,q\} \Leftrightarrow \{p \land q\}$ and $\{q\} \Leftrightarrow \{q\}$, but $\{p,q\} \cap \{q\}=\{q\}$ whereas $\{p \land q\} \cap \{q\}=\emptyset$, they are not logical equivalent, thus $\Leftrightarrow$ is not a congruence again... So let me rollback the old definition, under that $\frak F(\mathcal L)/\Leftrightarrow$ can be sure a complete lattice.
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
But now is $\Leftrightarrow$ still a congruence? It's a question...
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
@MihaHabič Okay, thank you. I have rewritten (2') that $\Phi \lor \Psi=\Phi \cap \Psi$, then $\frak F(\mathcal L)$ is a complete lattice too.
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
added 5 characters in body
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Let me reconsider it.
Mar
27
comment What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
@MihaHabič Yes.
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
correctify
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Update
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Update
Mar
27
revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces?
Update