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The Herbrand topos

Published online by Cambridge University Press:  04 June 2013

BENNO VAN DEN BERG
BENNO VAN DEN BERG*
Affiliation:
Mathematisch Instituut, Utrecht University, PO. Box 80010, 3508 TA Utrecht, The Netherlands. e-mail: [email protected]
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Abstract

We define a new topos, the Herbrand topos, inspired by the modified realizability topos and our earlier work on Herbrand realizability. We also introduce the category of Herbrand assemblies and characterise these as the ¬¬-separated objects in the Herbrand topos. In addition, we show that the category of sets is included as the category of ¬¬-sheaves and prove that the inclusion functor preserves and reflects validity of first-order formulas.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 361 - 374
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

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