Realizability Models Separating Various Fan Theorems
Robert S. Lubarsky, Michael Rathjen
TL;DR
This paper constructs a realizability model based on reals within a countable ideal of Turing degrees to demonstrate separations among different variants of the Fan Theorem.
Contribution
It introduces a new realizability model using reals in a countable ideal of Turing degrees to analyze Fan Theorem variants.
Findings
Separation results among Fan Theorem variants
Development of a realizability model based on Turing degrees
Application of the model to prove logical distinctions
Abstract
We develop a realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving variants of the Fan Theorem.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · semigroups and automata theory