How did it go with Mr. Wild?

A bit stuttered.

Stuttered? Okay, can we end it? What happened?

I think we have a lot of stuttered material.

Okay, so are there any questions about the material?

The uncertainty must have been due to full-scale models via PCP.

And the lack of expression of reachability over infinite models by means of compactness.

There was the problem with the formula. It says there is a formula.

And Paul wanted to write the formula.

Oh, the formula that says something is reachable in steps.

Is this the number we are counting on?

There are more.

I know one more.

You know at least two.

Okay, so we are waiting for a total of three or two?

I think it's a difference.

Okay, then two.

But he was just on the phone. He was at 10.

Okay, so not our fault.

What does the issue look like next Monday? Is everything feasible?

Is the paper understood? Does that fit? Are there any questions about the paper?

Okay.

It says once that the O.L. is not decisive.

That means the validity is not decisive.

Yes, it doesn't matter because I can reduce validity and reachability.

So whether the validity is decisive or the reachability is not important.

But validity is the right reading style.

Okay, then.

So we can play now.

To be more precise, we are going to play for a while with the so-called wet-free sea.

Our goal is to develop some techniques, which we have just seen, with the non-expression of reachability.

Or at least to get a grip on the expression strength of full.

Not only over infinite, but also limited to infinite models.

In the theory of first order logic over unrestricted models, i.e. possible infinite models, this compactness plays a central role.

Compactness allows you to build models on a stroke, simply because you can write infinite formulas.

Then you say, well, that's apparently finally achievable, so I get a model that fulfills the entire formula.

So that's a model theoretical miracle that you just demand the completeness.

And that is not available over finite models. That's why the entire known model theory is broken, as you can see in Schankisler or something like that.

So that's why this is a special branch of logic research that is of special interest to computer science.

In short, finite model theory is a database theory.

A database is a heap of information about a lot of individuals.

I can't get a lot of individuals in a database like that.

It tells me which relations exist between these individuals, i.e. the one who owns the house on Goethe Street 23 and so on.

In this respect, it is simply a finite structure of first order logic.

A model for certain signatures in first order logic.

And these signatures are called database schemas.

So now I'll simplify a little.

So that means that if I want to run a model theory, i.e. the theory in such databases and things that I can say about it,

also queries that I can run on it, queries are nothing but first order formulas with open variables.

The amount of fulfillment of such a first order formula with open variables is the result of my query modulo 1.5 syntax things