## Paul Blain Levy - A Ghost at $\omega_1$

lmcs:2626 - Logical Methods in Computer Science, July 26, 2018, Volume 14, Issue 3 - https://doi.org/10.23638/LMCS-14(3:4)2018
A Ghost at $\omega_1$

Authors: Paul Blain Levy

In the final chain of the countable powerset functor, we show that the set at index $\omega_1$, regarded as a transition system, is not strongly extensional because it contains a "ghost" element that has no successor even though its component at each successor index is inhabited. The method, adapted from a construction of Forti and Honsell, also gives ghosts at larger ordinals in the final chain of other subfunctors of the powerset functor. This leads to a precise description of which sets in these final chains are strongly extensional.

Volume: Volume 14, Issue 3
Published on: July 26, 2018
Accepted on: July 26, 2018
Submitted on: January 2, 2017
Keywords: Computer Science - Logic in Computer Science,03E75