Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The effect of forcing axioms on the tightness of the $G_\delta$
  modification   We show that $\mathsf{PFA}$ implies that the tightness $t(X_\delta)$ of the
$G_\delta$-modification of a Fr\'echet $\alpha_1$-space $X$ is at most
$\omega_1$, while $\Box(\kappa)$ implies that there is a Fr\'echet
$\alpha_1$-space with $G_\delta$-tightness equal to $\kappa$. We use the
example constructed from $\Box(\kappa)$ to show that a local version of the
bound $t(X_\delta)\le 2^{t(X)L(X)}$ does not hold. We also construct, assuming
$\mathsf{MA}$, an example of a Fr\'echet space whose $G_\delta$-tightness is
larger than $\omega_1$.

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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex