Skip to main content Accessibility help
×
Home

SHEAF RECURSION AND A SEPARATION THEOREM

  • NATHANAEL LEEDOM ACKERMAN (a1)

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 tree.

Copyright

References

Hide All
[1]Barwise, Jon, Admissible sets and structures, Springer-Verlag, Berlin, 1975, An approach to definability theory, Perspectives in Mathematical Logic.
[2]Lars Birkedal, , Møgelberg, Rasmus Ejlers, Schwinghammer, Jan, and Støvring, Kristian. First steps in synthetic guarded domain theory: Step-indexing in the topos of trees. Logical Methods in Computer Science, vol. 8 (2012), no. 4, pp. 4:1, 45.
[3]Gianantonio, Pietro Di and Miculan, Marino, Unifying recursive and co-recursive definitions in sheaf categories, Foundations of software science and computation structures, Lecture Notes in Computer Science, vol. 2987, Springer, Berlin, 2004, pp. 136150.
[4]Jech, Thomas, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003, The third millennium edition, revised and expanded.
[5]Kasangian, Stefano and Vigna, Sebastiano, The topos of labelled trees: A categorical semantics for SCCS. Fundamenta Informaticae, vol. 32 (1997), no. 1, pp. 2745.
[6]Mac Lane, Saunders, Categories for the working mathematician, second ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998.
[7]Lane, Saunders Mac and Moerdijk, Ieke, Sheaves in geometry and logic, Universitext, Springer-Verlag, New York, 1994. A first introduction to topos theory, Corrected reprint of the 1992 edition.
[8]Moschovakis, Yiannis N., Descriptive set theory, second ed., Mathematical Surveys and Monographs, vol. 155, American Mathematical Society, Providence, RI, 2009.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed