Sh:1088

• Shelah, S., & Steprāns, J. Universal graphs and functions on \omega_1. Annals of Pure and Applied Logic. To appear.
• Abstract:
  It is shown to be consistent with various values of \mathfrak{b} and \mathfrak{d} that there is a universal graph on \omega_1. Moreover, it is also shown that it is consistent that there is a ’ universal graph on \omega_1 - in other words, a universal symmetric function from \omega^2_1 to 2 – but no such function from \omega^2_1 to \omega. The method used relies on iterating well know reals, such as Miller and Laver reals, and alternating this with the PID forcing which adds no new reals.
• Version 2020-08-13 (39p)

@article{Sh:1088,
 author = {Shelah, Saharon and Stepr{\={a}}ns, Juris},
 title = {{Universal graphs and functions on $\omega_1$}},
 journal = {Annals of Pure and Applied Logic},
 year = {to appear}
}