What was the title of Alan Turing's doctoral dissertation?

The title of Alan Turing’s doctoral dissertation was Systems of Logic Based on Ordinals. He completed the dissertation at Princeton University in 1938 under the supervision of the mathematician and logician Alonzo Church.

The work explored how formal systems of mathematics could be extended through ordinal logic. Turing was responding in part to Gödel’s incompleteness results, which showed that sufficiently powerful formal systems contain true statements that cannot be proved within those systems. His dissertation examined ways of building progressively stronger systems by adding new principles.

The title is sometimes confused with Turing’s earlier paper On Computable Numbers, which introduced the abstract concept now known as the Turing machine, or with Computing Machinery and Intelligence, his 1950 paper about machine intelligence and the imitation game. The dissertation was later published in the Proceedings of the London Mathematical Society in 1939.