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The Herbrand topos
Published online by Cambridge University Press: 04 June 2013
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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