Characterizing partitioned assemblies and realizability toposes
Jonas Frey
TL;DR
This paper provides straightforward characterizations of partitioned assemblies and realizability toposes over partial combinatory algebras, offering an extensional perspective on their structure and properties.
Contribution
It introduces simple, extensional characterizations of partitioned assemblies and realizability toposes, advancing the understanding of their foundational structure.
Findings
Provides extensional characterizations of PAsm(A) and RT(A)
Answers open questions about realizability toposes
Simplifies the understanding of realizability toposes' structure
Abstract
We give simple characterizations of the category PAsm(A) of partitioned assemblies, and of the realizability topos RT(A) over a partial combinatory algebra A. This answers the question for an 'extensional characterization' of realizability toposes.
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Taxonomy
TopicsLogic, programming, and type systems · Homotopy and Cohomology in Algebraic Topology · Logic, Reasoning, and Knowledge