I'm looking for an inverse system $(X_\alpha)_{\alpha < \omega_1}$ of vector spaces (EDIT: over a finite field) such that, for some $\lambda \geq 2$ with $\lambda < \lambda^{\omega_1}$ (I believe the case where $\lambda = \kappa^\omega$ for some $\kappa \geq 2$ is particularly interesting), the f...

Continuum Hypothesis says that every infinite cardinal smaller than $2^{\aleph_0}$ is equal to $\aleph_0$. In the other hand I've heard that Martin Axiom says that these cardinals are "similar" in some sense (and that's a quote from Polish Wikipedia). What exactly does it mean? I couldn't find an...