Logic Question

Stream: maths

[Racky Dichminky]

I have a bit general question out here on logic:

On a more serious note, do you know any nice arguments concerning when we can extend results of the form "chain of length $\mu_0$ where $\mu_0$ is minimal such that $2^{\mu_0} > \lambda$ to "chain of length $\lambda$"?

Preferably in reference to stability

[Racky Dichminky]

Racky Dichminky said:

I have a bit general question out here on logic:

do you know any nice arguments concerning when we can extend results of the form "chain of length $\mu_0$ where $\mu_0$ is minimal such that $2^{\mu_0} > \lambda$ to "chain of length $\lambda$"?

Preferably in reference to stability

$\mu_0$ and $\lambda$ will be cardinals - and yes, it's about model-theoretic stability. An example: a lot of the time we are concerned about building trees level by level, and we violate stability at $\lambda$ by building a tree of height $\mu_0$. The question is then if we have a tree of height $\mu_0$ (violating stability), can we extend this tree to a tree of height $\lambda$. Part of the motivation here is that under GCH, $\mu_0 = \lambda$.

I hope the question is clear now :)

[Kevin Buzzard]

This is a forum for questions about the lean theorem prover. Have you tried mathoverflow?