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 Mar 27 revised What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces? deleted 21 characters in body Mar 27 asked What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces? Mar 24 accepted How to extend definition of n-tuple to the case $n=0$? Mar 23 comment How to extend definition of n-tuple to the case $n=0$? Well, if memory serves me right, the function from $n$, even $\alpha$, any transfinite ordinal, into $X$ is called a sequence over $X$. However the definition of sequence bases on the definition of function, which bases on the definition of relation, which is also bases on the definition of tuple... Thus the Kuratowski definition seems cannot be ignored if we don't want to cause a circular definition. Mar 22 asked How to extend definition of n-tuple to the case $n=0$? Mar 22 accepted Can proper classes also have cardinality? Mar 22 accepted On models of ZFC, does there exist a bijection between Von Neumann universe and the ordinal class? Mar 22 comment Can proper classes also have cardinality? Oh, this is only for classes of sets, so it needs to be reconsidered too. Mar 22 comment Can proper classes also have cardinality? In which $X,Y$ are unary predicate variable symbols of type (0), $F$ is a binary predicate variable symbol of type (0,0), and $Ep$ is a binary predicate symbol of type ((0),(0)). Mar 22 comment Can proper classes also have cardinality? No, I don't think this is a load of rubbish. Classes can be seen as unary relations over the set model, so maybe we can talk about it with Higher-order language. In detail, seems we can define it by $$Ep(X,Y) \leftrightarrow \exists F(\forall x \forall y\forall y'( F(x,y) \land F(x,y') \to y=y') \land \forall x \forall y (F(x,y) \to X(x) \wedge Y(y)) \land \forall x (X(x) \to \exists! y (Y(y) \land F(x,y))) \land \forall y (Y(y) \to \exists! x(X(x) \land F(x,y))))$$ Mar 22 revised Can proper classes also have cardinality? fix Mar 22 comment Can proper classes also have cardinality? Well, seems you are right. Besides, can the universe about cardinals of classes be argued within NBG? It seems in that proper classes can be talked easier Mar 21 revised Can proper classes also have cardinality? added 19 characters in body Mar 21 asked Can proper classes also have cardinality? Mar 21 comment On models of ZFC, does there exist a bijection between Von Neumann universe and the ordinal class? V=L seems so strong, many axioms(like GCH, also CH) follow it. Mar 21 asked On models of ZFC, does there exist a bijection between Von Neumann universe and the ordinal class? Mar 20 comment What is a “secular equation”? It's helpful. Thank you. Mar 20 comment What is a “secular equation”? Why it is called secular equation? Is there also a sacred equation? Mar 14 revised Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$ fixed grammar Mar 13 revised Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$ added 1 characters in body