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17h
accepted Finite complement topology over $\Bbb{R}$ is not second-countable under ZF?
17h
asked Finite complement topology over $\Bbb{R}$ is not second-countable under ZF?
Apr
10
comment Infinite palindromes in number of nonisomorphic posets is independent of $\mathsf{ZF}$
In the book author wrote in the solutions section: "The purpose of this seemingly frivolous exercise is to point out that some simply stated facts about posets may be forever unknowable." I think there is no known proofs.
Apr
9
comment Algebraic extensions help please?
If $B$ is a basis of $K$ as $F$-vector space then $B$ spans the $F(u)$-vector space $K(u)$.
Apr
9
answered Write an inductive proof that if there is a surjection $ f : \lceil m \rceil → \lceil n \rceil $ then $m ≥ n$.
Apr
8
comment if $\mathfrak{B} \vDash BA$ then $S(B)$ is a stone space.
What is $BA$?$\!$
Apr
8
answered Why is $S = \{ x \in \mathbb{Q} | 2 < x^2 < 3 \}$ closed in $\mathbb{Q}$?
Apr
7
revised “Direct sums of injective modules over Noetherian ring is injective” and its analogue
deleted 1 character in body
Apr
7
comment How to prove every partition of same cardinality sets has same cardinality?
@Maddy Since every ordinal has its unique Cantor normal form.
Apr
7
answered How to prove every partition of same cardinality sets has same cardinality?
Apr
6
accepted “Direct sums of injective modules over Noetherian ring is injective” and its analogue
Apr
6
asked “Direct sums of injective modules over Noetherian ring is injective” and its analogue
Apr
1
comment Decidability of the cardinality of a set given that the Continuum Hypothesis is independent from ZFC
What is the "undecidable cardinality"? Every set has a its own cardinality even if we don't know what the cardinality of the given set is $\aleph_1$, $\aleph_3$ or $\aleph_{39}$.
Mar
31
accepted Can we find two numbers from $n+2$ numbers chosen from $\{1,2,3,\cdots\}$?
Mar
31
comment Can we find two numbers from $n+2$ numbers chosen from $\{1,2,3,\cdots\}$?
@MichaelBurr I know it, but if $n+2$ numbers are chosen and no numbers contained from same $\{k,2n-1+k\}$ then at least one number lies between $n+2$ and $2n-1$ and I try to use it.
Mar
31
asked Can we find two numbers from $n+2$ numbers chosen from $\{1,2,3,\cdots\}$?
Mar
30
comment Power Set of a Power Empty Set
The number of elements in the power set of $n$-element set is $2^n$.
Mar
30
comment Does elementary equivalence imply L-equivalence for structure L?
Could you explain what the L-equivalence is?
Mar
30
comment Power Set of a Power Empty Set
The number of elements of $PPP(\varnothing)$ is 4, so your set should have 4 elements (but curly brackets confuses me.)
Mar
30
comment $\sf ZF$ — Sets that can be proven to exist
Despite of the undefinability of definablilty, I think your reasoning are pretty fine. You can avoid the problem trickily by using formalized satisfaction relation and you can collect the set of all definable elements in the given model of ZFC. I don't know it gives a model of ZFC and maybe experts gives an answer.