Polarized partitions on the second level of the projective hierarchy

Jörg Brendle, Yurii Khomskii
2012 Annals of Pure and Applied Logic  
A subset A of the Baire space ω ω satisfies the polarized partition property if there is an infinite It satisfies the bounded polarized partition property if, in addition, the H i are bounded by some pre-determined recursive function. Di Prisco and Todorčević (2003) [6] proved that both partition properties are true for analytic sets A. In this paper we investigate these properties on the 1 2 -and 1 2 -levels of the projective hierarchy, i.e., we investigate the strength of the statements "all
more » ... 2 / 1 2 sets satisfy the (bounded) polarized partition property" and compare it to similar statements involving other well-known regularity properties.
doi:10.1016/j.apal.2012.03.003 fatcat:j4wwvq6ek5gmjj77k2xzqtmaqe