Date of Award
Spring 6-2025
Document Type
Thesis (Ph.D.)
Department or Program
Mathematics
First Advisor
François Dorais
Second Advisor
Marcia Groszek
Abstract
We construct an interpretation of higher types into Peano arithmetic, showing in particular that every model of PA is a model of higher types. This is a reversal of Gödel’s Dialectica construction. We also define the classifier degrees, a degree structure which subsumes the Turing degrees, the enumeration degrees, and the many-one degrees. The classifier degrees boast a rich structure and many well-behaved operations.
Recommended Citation
Logsdon, Benjamin Carrick, "A Realizability Approach to Constructing Higher Types via Classifiers" (2025). Dartmouth College Ph.D Dissertations. 351.
https://digitalcommons.dartmouth.edu/dissertations/351
