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The axiom $W_\kappa$, for $\kappa$ a cardinal, is the statement that for all sets $X$, either $|X|\leq\kappa$ (that is, there is an injection $X\to\kappa$) or $\kappa\leq|X|$. Is there literature on t …

For a set $X$, the Lindenbaum number of $X$, $\aleph^*(X)$, is the least non-zero ordinal $\alpha$ such that there is no surjection $X\to\alpha$. It seems to be well-known that for infinite sets $X$ a …

Are there models of ZFC in which $\mathfrak{r}$ is strictly less than $\mathfrak{s}$? I've not been able to find any forcings that end up with this result. Here $\mathfrak{r}$ is the reaping number $\ …

I am interested in better understanding the following property: Let us say that an iteration of forcings $\langle\mathbb{P}_\alpha,\dot{\mathbb{Q}}_\beta\mid\alpha\leq\gamma,\beta<\gamma\rangle$ is $\ …

In Kunen [1] the author makes the following note: Let $\kappa$ be measurable with normal measure $\mathscr{U}$ in a model of $\mathsf{GCH}$. Let $\mathbb{P}$ be an iteration of $\operatorname{Add}(\al …

I have come across the following notion of (what I am calling) dual ideals, and I am looking for any work in which this notion has been considered, and particularly anything about transferring propert …