Zulip Chat Archive

Stream: maths

Topic: Logic Question


Racky Dichminky (Oct 01 2022 at 07:11):

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 μ0\mu_0 where μ0\mu_0 is minimal such that 2μ0>λ2^{\mu_0} > \lambda to "chain of length λ\lambda"?

Preferably in reference to stability

Racky Dichminky (Oct 01 2022 at 23:24):

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 μ0\mu_0 where μ0\mu_0 is minimal such that 2μ0>λ2^{\mu_0} > \lambda to "chain of length λ\lambda"?

Preferably in reference to stability

μ0\mu_0 and λ\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 λ\lambda by building a tree of height μ0\mu_0. The question is then if we have a tree of height μ0\mu_0 (violating stability), can we extend this tree to a tree of height λ\lambda. Part of the motivation here is that under GCH, μ0=λ\mu_0 = \lambda.

I hope the question is clear now :)

Kevin Buzzard (Oct 02 2022 at 00:23):

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


Last updated: Dec 20 2023 at 11:08 UTC