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location Unknow Galaxy
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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.


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