you

you

you

you

you

hello prof can you hear me

you

hello

I think what is happening

I think we need to reach out to someone who is in the class and tell through him or her we need to let him know that we cannot hear anything

hello

hello

I'm

you

can hear me now?

yes we can, now

can you hear me now?

yes

yes?

yes, yes

okay, I have no idea why it works, but that's great

thanks for the feedback

okay

good, I'll also

just

okay

good, so we have

this universe

and basically we need to have a separate set for everything we have, for every type we have, that's why it's indexed with a t

so we could for example say

for type alpha we have some steps

for example it could be the numbers 1, 2, 3 and so on

we need

we have type beta as well, so we need something for the

beta

I could say there's two values, I can pick anything by one

for functions we need things as well

and so far our definition says we could pick anything we want, like I could pick numbers again

but if you think about it, that's sort of stupid

these are supposed to be functions of type alpha to beta, doesn't work with numbers

and that's why we have this extra restriction, where we say well actually

the elements of the set for functions should be functions that match in the types

so I have to put some kind of function that maps

numbers to truth values effectively

I don't know, I could say this prime, that's a function that we shouldn't prove, it's a prime number, otherwise it's false

maybe it's even, whatever, let's set

so that's our universe, that's the things we will map things to

and now we have an interpretation function i

where we take the things from our signature, which I didn't write down yet

so our signature says c is a constant of type alpha, so we have something like sigma