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Let FOO = BLAH $\otimes$ BLEELG.

 

Remember that BLAH completely characterizes the FLEEN (Thm. 11.36); meanwhile, bringing BLEELG prevents VORPiness.

Let FOO = BLAH $\otimes$ BLEELG.

Remember that BLAH completely characterizes the FLEEN (Thm. 11.36); meanwhile, bringing BLEELG prevents VORPiness.

Second, I've provided nontrivial explicit examples of everything. Moreover, I haven't tried to mix notations to be more efficient (e.g. $\{X_1=\{\{2,3\},\{2,4\},\{3,4\}\}, etc.\}$) - the only thing I've done is throw in some spacing for readability. This helps the reader both understand your definition and repair it if you have made any errors.

Second, I've provided nontrivial explicit examples of everything. Moreover, I haven't tried to mix notations to be more efficient - the only thing I've done is throw in some spacing for readability (which is actually quite useful in some situations, and sets-of-sets is one of those since the curly braces can blur together). This helps the reader both understand your definition and repair it if you have made any errors.

Suppose I have a set $S$ and a natural number $m$. For $i\in S$, let $$X_i=\{a\subseteq S: \vert a\vert=m\mbox{ and }i\not\in a\}.$$ We then let the $m$-crown of $S$ be the set $$\{X_i: i\in S\}.$$ For example, if $S=\{1,2,3,4\}$ and $m=2$ then e.g. $$X_2=\{\{1,3\}, \{1,4\}, \{3,4\}\},$$ and the whole $m$-crown of $S$ is $$\{$$ $$\{\{2,3\}, \{2,4\}, \{3,4\}\},$$ $$\{\{1,3\}, \{1,4\}, \{3,4\}\},$$ $$\{\{1,2\}, \{1,4\}, \{2,4\}\},$$ $$\{\{1,2\}, \{1,3\}, \{2,3\}\}$$ $$\}.$$

Suppose I have a set $S$ and a natural number $m$. For $i\in S$, let $$X_i=\{a\subseteq S: \vert a\vert=m\mbox{ and }i\not\in a\}.$$ We then let the $m$-crown of $S$ be the indexed set (with indexing set $S$ itself) $$(X_i)_{i\in S}.$$ For example, if $S=\{1,2,3,4\}$ and $m=2$ then e.g. $$X_2=\{\{1,3\}, \{1,4\}, \{3,4\}\},$$ and the whole $m$-crown of $S$ is $$($$ $$X_1=\{\{2,3\}, \{2,4\}, \{3,4\}\},$$ $$X_2=\{\{1,3\}, \{1,4\}, \{3,4\}\},$$ $$X_3=\{\{1,2\}, \{1,4\}, \{2,4\}\},$$ $$X_4=\{\{1,2\}, \{1,3\}, \{2,3\}\}$$ $$).$$