Special Session
The Π21-spectrum conjecture
On-site
The Π21-soundness ordinal of a theory T, denoted o21(T), is a measure of how close T is to being Π21-correct. The Π21-spectrum conjecture asserts that the possible values of o21(T) for recursively enumerable extensions of ACA0 are precisely the Σ11-definable epsilon numbers. In this talk, we present a proof of the following theorem, which is formalizable in weak set theories: If the Π21-Spectrum Conjecture fails, then Second-Order Arithmetic is consistent. This is joint work with Fedor Pakhomov.
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