# not sure what these basic FO symbols mean [closed]

I know some basic logic symbols, but i'm not sure what this formula means:

Fragment: http://i35.tinypic.com/14jt1n9.png

in particular, what is the subscript "1<=i

and the N with the A superscript. the multiple typefaces of "A".

this is beyond the basic and/or/exists/forall that i know in basic logic

is there a statement of this formula and its conditions in english words?

Thanks!

Updated: oops my bad, I should've read the part where they defined it!

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Most of the definitions about $A$ in various fonts and ${\cal N}_r^{\cal A}$ you are looking for are at the top of page 3 of the article. The subscript $1\le i\lt j\le k$ just indicates which combinations of $i$ and $j$ are included in the conjunction.