Linked Questions
10 questions linked to/from The property of the dense subfilter of a selective ultrafilter
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Examples of common false beliefs in mathematics
The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...
5
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1
answer
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Relation between ultrafilters ${\scr U}$ and ${\scr U} \otimes {\scr U}$ [closed]
If ${\scr U}$ and ${\scr V}$ are ultrafilters on non-empty sets $A$ and $B$ respectively, then the tensor product ${\scr U}\otimes{\scr V}$ is the following ultrafilter on $A\times B$:
$$\big\{X\...
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3
votes
1
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Dense filter and selective ultrafilter
We say that $\rho(A)=\lim_{n\to\infty}\frac{|A\cap n|}{n}$ is the density of subset $A\subset\omega$ if the limit exists. Let us define the filter $\mathcal{F_1}=\{A\subset\omega~|~\rho(A)=1\}$.
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2
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Infinite products from the fake Laver tables-Now with no set theory
We say that a sequence of algebras $(\{1,\dots,2^{n}\},*_{n})_{n\in\omega}$ is an inverse system of fake Laver tables if for $x\in\{1,\dots,2^{n}\}$, we have
$2^{n}*_{n}x=x$,
$x*_{n}1=x+1\mod 2^{n}$,...
1
vote
1
answer
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Some kind of idempotence of dense filter
In discussion of following questions question1, question2, question3 became clear (see definitions in question3 ) that for the Frechet filter $\mathcal{N}$ we have $\mathcal{N}\nsim\mathcal{N}\otimes\...
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1
vote
0
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How many critical points can you have below a Fibonacci term in an algebra of elementary embeddings?
In this question, I asked about how slowly the Fibonacci terms in a algebra of elementary embeddings could grow, but I did not inquire if there was a limit to how quickly the Fibonacci terms could ...
1
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0
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Basic questions about varieties of uniformly partially permutative algebras
Define the Fibonacci terms $t_{n}(x,y)$ for all $n\geq 1$ by letting
$t_{1}(x,y)=y,t_{2}(x,y)=x,t_{n+2}(x,y)=t_{n+1}(x,y)*t_{n}(x,y)$.
We say that an algebra $(X,*)$ is $N$-uniformly partially ...
2
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0
answers
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Is the action of free self-distributive algebras on racks computable in polynomial time?
Let $B_{\infty}$ denote the infinite strand braid group. Let
$\mathrm{sh}:B_{\infty}\rightarrow B_{\infty}$ be the mapping where
$\mathrm{sh}(\sigma_{i})=\sigma_{i+1}$ whenever $i\geq 1$. Then
$B_{\...
2
votes
0
answers
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Does shifted conjugacy still give you free self-distributive algebras on one generator for quotient groups of the braid groups?
Let $B_{\infty}$ denote the infinite strand braid group. Let $\mathrm{sh}:B_{\infty}\rightarrow B_{\infty}$ be the group homomorphism where $\mathrm{sh}(\sigma_{i})=\sigma_{i+1}$ for all $i>0$.
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2
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1
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Dense subfilter of selective ultrafilter
Given selective ultrafilter $\mathcal{U}$ on $\omega$ and dense filter $\mathcal{F_1}=\{A\subset\omega~|~\rho(A)=1\}$, where $\rho(A)=\lim_{n\to\infty}\frac{|A\cap n|}{n}$ if the limit exists. Let $\...
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