Can Selective Spell be used to exclude a swarm from targeting?

I’m researching the attack spells available to druids. Creeping Doom looks very useful for some situations, but it seems like it doesn’t combine well with other spells like Flame Strike and Fire Storm since you’ll quickly destroy your own swarms. Can a druid use Selective Spell to mitigate this by excluding the swarms?

Filter not working in Selective Forwarding Gmail

So, I have here a more than a hundred clients’ email addresses that I wish to forward selective emails to what I call “Master” email. So I won’t have to open them one by one just to check if there was an update from the specific filter I set.

FILTERS I used that are both separated by OR operator:

From – (10 different emails)

Has the words – (11 related keywords, but all different contexts)

Reason being for 10 different emails is that the sender kept on creating a new email if their system is down or email has insufficient space. That said, I tried creating filters without filling out the FROM field just to see if emails could be forwarded on filter “Has the words” alone, but to no avail. It didn’t work.

Also, correct me if I’m wrong. I happen to find out that more than 8 keywords will not work. I had to divide the keywords in that case.

When all is divided, still it doesn’t forward now that I have two different filters both forwarding to my master email.

How to solve this problem?

Existance of bijective function which maps tensor product of subsets of a selective ultrafilter into the ultrafilter

In the answer on this question Andreas Blass had shown that for any selective ultrafilter $ \scr{U}$ on $ \omega$ and for any free subfilter $ \scr{F}\subset{U}$ doesn’t exist bijection $ \varphi:\omega^2\to\omega$ such that $ \varphi(\scr{F}\otimes\scr{F})\subset\scr{U}$ . Thus I am trying to weaken the conditions.

Question: Does there exist a pair of subsets $ \scr{A},\scr{B}$ of selective ultrafilter $ \scr{U}$ on $ \omega$ and a bijection $ \varphi:\omega^2\to\omega$ with following properties:

  1. $ \scr{A}$ and $ \scr{B}$ have finite intersections property and $ \cap\scr{A}=\cap\scr{B}=\varnothing$
  2. $ \varphi(\scr{A}\otimes\scr{B})\subset\scr{U}$ ?

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 $ \mathcal{F}=\mathcal{F_1}\cap\mathcal{U}$ .

Question: Does there exist a family $ \{A_i\subset\omega\}_{i<\omega},~A_i=\{a_{ik}\}_{k<\omega}$ of pairwise disjoint subsets such that for any $ B\in\mathcal{F}$ we have: $ $ \{a_{ik}~|~i,k\in B\}\in\mathcal{U} $ $

Remark: The question is equivalent formulation of this one which still has no answer.

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\}$ .

Question: Is there exists (in ZFC & CH) selective ultrafilter $ \mathcal{U}$ and a bijection $ \varphi:\omega\to\omega$ such that $ \varphi(\mathcal{F_1})\subset\mathcal{U}$ ?

Remark: Someone had downvoted two similar questions. Please, explane what is wrong if something is wrong

The property of a dense subfilter of a selective ultrafilter

Let us define the density of subset $ A\subset\omega$ : $ $ \rho(A)=\lim_{n\to\infty}\frac{|A\cap n|}{n}$ $ if the limit exists. Let $ \mathcal{F_1}=\{A\subset\omega~|~\rho(A)=1\}$ . $ \mathcal{F_1}$ is the filter and for the Frechet filter we have $ \mathcal{N}\subset\mathcal{F_1}$ . For arbitrary selective ultrafilter $ \mathcal{U}$ let $ \mathcal{F}=\mathcal{F_1}\cap\mathcal{U}$ .

Question: is there exists a bijection $ \varphi:\omega\times\omega\to\omega$ such that $ $ \varphi(\mathcal{F}\otimes\mathcal{F})\subset\mathcal{U} $ $