Albert Visser

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3 papers · 1 filter

math.LO2026

On a Theorem by Bezboruah & Shepherdson

Albert Visser

We discuss an incompleteness result proven by Bezboruah and Shepherdson. This result tells us that the weak theory $PA^{-}$ does not prove the consistency of any theory (under…

math.LO2025

Extensional Independence

Taishi Kurahashi, Albert Visser

Joel Hamkins asks whether there is a $Π_{1}^{0}$ -formula $ρ (x)$ such that $ρ (ϕ)$ is independent over $PA + ϕ$ , if this theory is consistent, where this construction is extensional…

math.LO2025

On a Question of Hamkins'

Albert Visser

Joel Hamkins asks whether there is a $Π_{1}^{0}$ -formula $ρ (x)$ such that $ρ (┌ ϕ ┐)$ is independent over $PA + ϕ$ , if this theory is consistent, where this constru…