PP201109: Brendle, Jörg and Khomskii, Yurii (2011) Polarized partitions on the second level of the projective hierarchy. [Report]

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Abstract
A subset $A$ of the Baire space satisfies the "polarized partition property" if there is an infinite sequence $< H_i  i \in \omega >$ of finite subsets of $\omega$, with $H_i \geq 2$, such that $\prod_i H_i \subseteq A$ or $\prod_i H_i \cap A = \varnothing$. It satisfies the "bounded polarized partition property" if, in addition, the $H_i$ are bounded by some predetermined recursive function. DiPrisco and Todorcevic proved that both partition properties are true for analytic sets. In this paper we investigate these properties on the $\Delta^1_2$ and $\Sigma^1_2$levels of the projective hierarchy, i.e., we investigate the strength of the statements "all $\Delta^1_2$ / $\Sigma^1_2$ sets satisfy the (bounded) polarized partition property" and compare it to similar statements involving other wellknown regularity properties.
Item Type:  Report 

Report Nr:  PP201109 
Series Name:  Prepublication (PP) Series 
Year:  2011 
Uncontrolled Keywords:  polarized partitions; projective hierarchy; descriptive set theory 
Date Deposited:  12 Oct 2016 14:37 
Last Modified:  12 Oct 2016 14:37 
URI:  https://eprints.illc.uva.nl/id/eprint/413 
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