SHEAF RECURSION AND A SEPARATION THEOREM
@article{Ackerman2014SHEAFRA,
title={SHEAF RECURSION AND A SEPARATION THEOREM},
author={Nathanael Leedom Ackerman},
journal={The Journal of Symbolic Logic},
year={2014},
volume={79},
pages={882 - 907}
}Abstract Define a second order tree to be a map between trees (with fixed codomain). We show that many properties of ordinary trees have analogs for second order trees. In particular, we show that there is a notion of “definition by recursion on a well-founded second order tree” which generalizes “definition by transfinite recursion”. We then use this new notion of definition by recursion to prove an analog of Lusin’s Separation theorem for closure spaces of global sections of a second order…
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