[FOM] Two Questions About Second-order Branching Quantifiers

[Thomas Forster]

There's a theorem about this in the literature, connecting branching 
quantifiers to NP formulae.  No doubt others will be quick off the mark
with the details.  I have a student about to start work on this stuff, and 
it has been much on my mind.


As for how to write these things in LaTeX you might find this illustration 
useful.



\begin{equation}\label{eqn2}
  \left(
  \begin{array}{r}
      \forall x \exists y \\
      \forall x'\exists y' \\
       \end{array}\right)
  \left( (x = x' \to y = y') \wedge R(x,y) \wedge R(x',y') 
\right)\end{equation}


If anyone has a better way i'd be glad to learn of it.

     tf



On 
Fri, 26 Jan 2007, Richard Heck wrote:

> 
> As said.
> 
> (1) Consider a very simple branching structure
>     (EF)
> 	B_xy(Fx,Gy,z)
>     (AG)
> Every such formula is clearly \Delta^1_1. Is it also the case that every
> \Delta^1_1 formula is equivalent to some such simple branching formula? If
> not, what is the strength of a system (semantically characterized, for now)
> admitting comprehension for such formulae?
> 
> (2) Does anyone know a good way to do branching quantifiers in LaTeX?
> 
> Richard Heck
> 
> 

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