# Tagged Questions

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### A special filter on cartesian product of sets

The following is inspired by this article in nLab (in attempt to simplify it using my notions of funcoids and reloids, which notation is however outside of the scope of this question). Fix a set $U$. ...
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### A totally bounded uniformity and certain filters

Conjecture For every totally bounded uniform space $(U;F)$ and filters $\mathcal{X}$, $\mathcal{Y}$ on $U$ such that $$\forall E\in F,X\in\mathcal{X},Y\in\mathcal{Y}:(X\times Y)\cap E\ne\emptyset,$$ ...
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### What is the cardinality of an element of an free ultrafilter?

Let $U$ be a free ultrafilter on a set $X$. I want to prove that the cardinality of every element $u\in U$ is equipotent to $X$. Is that true? Or does it lack some hypothesis?
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### Ramsey ultrapowers: any interesting properties?

A Ramsey ultrafilter is a free ultrafilter $D$ on $\omega$ such that for any partition of $\omega$ into subsets, none of which is in $D$, there exists a set in $D$ that intersects each member of the ...
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### Existence of a specific type of ultrafilter

Does there exist an ultrafilter $\omega$ on $N$ with the following property: $\forall A \in \omega$ we have that $kA \in \omega$ for a fixed $k \in N$. Where $kA = \{ka : a \in A\}$. I do not ...
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### Uniform normal filter on $\kappa$ is $\kappa$-complete and contains the club filter.

The question reads: Edit: The definition for uniform filter I was given is as follows: A filter $\mathcal{F}$ on $\kappa$ is uniform iff $\mathcal{F}$ contains all co-bounded sets in $\kappa$ iff ...
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### A follow up question on completeness of filter (generalised to p.o.s)

Now I'm looking at the following generalisation of $\kappa$-closedness of a filter on a set to a filter in a partial order: Let $\kappa$ be a regular uncountable cardinal. A partial order $P$ is ...
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### Question about definition of $\kappa$-completeness of filter

I am looking at the following definition: Let $\kappa$ be a regular uncountable cardinal and let $\mathcal F$ be a filter on a non-empty set $X$. We say that $\mathcal F$ is $\kappa$-complete if ...
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### ultrafilter $\kappa$-complete

Let $A$ an infinite set, $D$ an ultrafilter on $A$ and $\kappa$ an infinite cardinal. I want to show the following : $D$ is $\kappa$-complete iff $\forall\tau<\kappa$ and $\forall$ partition ...
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(Show that)If $\mathscr{U}$ is an ultrafilter on $\omega$, then $\mathscr{U}$ contains a subset $A$ of lower density zero. (But) there is an ultrafilter on $\omega$ such that every $A \in ... 1answer 77 views ### Why is a p-point never the limit of a countable set of non-principal ultrafilters? There are several descriptions, but I think the following definition of p-point suits for now: A point such that the intersection of countably many neighbourhoods of it, is again a neighbourhood. ... 2answers 188 views ### Subset of a P-ideal need not be a P-ideal I was looking for examples showing that subset of a P-ideal is not necessary. I will post below a counterexample I was able to find. (I hope it is correct.) But I'd be glad to see other simple (or ... 2answers 97 views ### p-point ultrafilters on a countable linear order Suppose that$(P,\leq)$is a countably infinite linear ordering, and$U$is a p-point ultrafilter on$P$. Show that there is an$X\in U$such that$X$has order type$\omega$or$\omega^*$. (This is ... 1answer 95 views ### Do Ramsey idempotent ultrafilters exist? I was studying idempotent ultrafilters when I saw that no principal ultrafilter could ever be idempotent, because$\left\langle n \right\rangle \oplus \left\langle n \right\rangle = \left\langle 2n ...
http://en.m.wikipedia.org/wiki/Dimension_theorem#section_1 Let's first not assume any choice principle. Let $V$ be a vector space over a field $F$ and $\beta_1,\beta_2$ be bases for $V$. Suppose ...