Axioms and (counter)examples in synthetic domain theory

DOI10.1016/S0168-0072(00)00014-2zbMath0961.18006OpenAlexW2142922307WikidataQ114656181 ScholiaQ114656181MaRDI QIDQ1577485

Alex K. Simpson, Jaap van Oosten

Publication date: 16 May 2001

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-0072(00)00014-2

zbMATH Keywords

elementary topossynthetic domain theorycategories of domainsinternal logic

Mathematics Subject Classification ID

Semantics in the theory of computing (68Q55) Categorical logic, topoi (03G30) Topoi (18B25) Categorical semantics of formal languages (18C50) Abstract and axiomatic computability and recursion theory (03D75)

Related Items (4)

Computational adequacy for recursive types in models of intuitionistic set theory ⋮ Well-foundedness in realizability ⋮ A synthetic theory of sequential domains ⋮ A Convenient Category of Domains

Cites Work

• Two models of synthetic domain theory
• A presentation of the initial lift-algebra
• The modified realizability topos
• Sheaves in geometry and logic: a first introduction to topos theory
• New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic
• Inductive construction of repletion
• The sequentially realizable functionals
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• The Discrete Objects in the Effective Topos
• On a Topological Topos
• A uniform approach to domain theory in realizability models
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