Tootfinder

This https://arxiv.org/abs/2503.24207 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Definability of mad families of vector spaces and two local Ramsey theories
Let $E$ be a vector space over a countable field of dimension $\aleph_0$. Two infinite-dimensional subspaces $V,W \subseteq E$ are almost disjoint if $V \cap W$ is finite-dimensional. This paper provides some improvements on results about the definability of maximal almost disjoint families (mad families) of subspaces in [17]. We show that a full mad family of block subspaces exists assuming either $\frak{p} = \max\{\frak{b},\frak{s}\}$ or a positive answer to a problem in [17], improving Smyth…

This https://arxiv.org/abs/1610.02706 has been replaced.
link: https://scholar.google.com/scholar?q=a

Saccharinity with ccc
Using creature technology, we construct families of Suslin ccc non-sweet forcing notions $\mathbb Q$ such that $ZFC$ is equiconsistent with $ZF+$"every set of reals equals a Borel set modulo the $(\leq \aleph_1)$-closure of the null ideal associated with $\mathbb Q$"+"there is an $ω_1$-sequence of distinct reals". This answers a question of the second author and Kellner. As an application of independent interest, we also show how our forcing adds a new $Π^1_2$ singleton over $L$ without relyi…