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SHEAF RECURSION AND A SEPARATION THEOREM

Published online by Cambridge University Press:  18 August 2014

NATHANAEL LEEDOM ACKERMAN
NATHANAEL LEEDOM ACKERMAN*
Affiliation:
DEPARTMENT OF MATHEMATICS HARVARD UNIVERSITY ONE OXFORD STREET CAMBRIDGE, MA 02138, USAE-mail: nate@math.harvard.edu
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Abstract

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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 tree.

Keywords

TreesSheavesDefinition by RecursionClosure SpacesSeparation Theorems06A9918F2054A0554H05
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 3 , September 2014 , pp. 882 - 907
Copyright
Copyright © The Association for Symbolic Logic 2014 

References

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