Abstract
The paper explores the logical strength of Isbell's zig‐zag theorem using the framework of reverse mathematics. Working in , we show that is equivalent to Isbell's zig‐zag theorem for countable monoids: If B is a monoid extension of A, then is dominated by A if and only if b has a zig‐zag over A. Our proof of Isbell's zig‐zag theorem avoids use of strong comprehension axioms common in traditional proofs. We also analyze the strength of theorems concerning binary relations.
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