Is Polynomial Time Choiceless?

@inproceedings{Grdel2015IsPT,
  title={Is Polynomial Time Choiceless?},
  author={Erich Gr{\"a}del and Martin Grohe},
  booktitle={Fields of Logic and Computation II},
  year={2015}
}
A long time ago, Yuri Gurevich made precise the problem of whether there is a logic capturing polynomial-time on arbitrary finite structures, and conjectured that no such logic exists. This conjecture is still open. Nevertheless, together with Andreas Blass and Saharon Shelah, he has also proposed what still seems to be the most promising candidate for a logic for polynomial time, namely Choiceless Polynomial Time (with counting). We survey some recent results on this logic. 
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TLDR
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