# Sh:392

- Jech, T. J., & Shelah, S. (1991).
*A partition theorem for pairs of finite sets*. J. Amer. Math. Soc.,**4**(4), 647–656. arXiv: math/9201248 DOI: 10.2307/2939283 MR: 1122043 -
Abstract:

Every partition of [[\omega_1]^{<\omega}]^2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite character. - published version (10p)

Bib entry

@article{Sh:392, author = {Jech, Thomas J. and Shelah, Saharon}, title = {{A partition theorem for pairs of finite sets}}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {4}, number = {4}, year = {1991}, pages = {647--656}, issn = {0894-0347}, doi = {10.2307/2939283}, mrclass = {03E05 (03E35 04A20 05D10)}, mrnumber = {1122043}, mrreviewer = {Carlos A. Di Prisco}, doi = {10.2307/2939283}, note = {\href{https://arxiv.org/abs/math/9201248}{arXiv: math/9201248}}, arxiv_number = {math/9201248} }