In this thesis we investigate automorphisms of partial combinatory algebras and construct realizability models of constructive set theory. After some introductory and background material in chapters 1 and 2, we define in chapter 3 a generalisation of Kripke and realizability models of intuitionistic logic that we call Kripke realizability models. In chapters 4, 6 and 7 we then develop various realizability models of constructive set theory. We show in chapter 5 how to use these techniques to investigate the automorphisms of some partial combinatory algebras. In chapter 8 we use a Kripke realizability model to show that a property known as the existence property does not hold for the set theory CZF.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:590459 |
| Date | January 2012 |
| Creators | Swan, Andrew Wakelin |
| Publisher | University of Leeds |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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