# Integration described by first-order logic?

1. Aug 19, 2013

### schlynn

Is it possible, to describe a Riemann integral with just first-order logic? And if so could someone point me to somewhere that has such a description of it.

2. Aug 19, 2013

### CompuChip

As far as I know any description of integration requires some qualifier of the form "$\forall A \subset X$" which is not expressible in first order logic. But I'd be happy to be proven wrong!

3. Aug 19, 2013

### economicsnerd

I don't know much formal logic beyond my intro model theory class, but...

In my attempt to define it, I couldn't do it without being able to say $$\exists n\in\mathbb N:\exists x_1,...\exists x_n:\enspace...\text{''}$$ or $$\bigvee_{n=1}^\infty \exists x_1,...\exists x_n:\enspace...\text{''}$$ which isn't kosher in any version of FOL I know.