[FOM] Re: branching quantifiers

[Thomas Forster]

Thank you very much for this.  I know about Blass-Gurevich and the
NP-completeness.  And Fagin and Walkoe...  But - i repeat - what about
*width* of quantifier prefixes?  I think i have proved that every
$\forall_{2n}$ formula ($2n$ alternations of quantifiers with the first
block universal) is equivalent to a branching-quantifier formula whose  
prefix is of width $n$ and where every row is \forall^* \exists^*.  Is   
this known?
   
I didn't know about decidablity of the monadic fragment, tho' it doesn't
surprise me.  But what is the strength of the *polyadic* fragment
without
equality?

     Thomas Forster