# Sh:1088

- Shelah, S., & Steprāns, J. (2021).
*Universal graphs and functions on \omega_1*. Ann. Pure Appl. Logic,**172**(8), Paper No. 102986, 43. DOI: 10.1016/j.apal.2021.102986 MR: 4266242 -
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 2021-04-28 (37p) published version (43p)

Bib entry

@article{Sh:1088, author = {Shelah, Saharon and Stepr{\={a}}ns, Juris}, title = {{Universal graphs and functions on {$\omega_1$}}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {172}, number = {8}, year = {2021}, pages = {Paper No. 102986, 43}, issn = {0168-0072}, mrnumber = {4266242}, mrclass = {03E17 (03C30 03C50 03E35 03E65)}, doi = {10.1016/j.apal.2021.102986} }