Summary: CHAPTER VI
G¨odel's Functional ("Dialectica") Interpretation
Jeremy Avigad
Department of Philosophy, Carnegie Mellon University
Pittsburgh, PA 15213
Solomon Feferman
Departments of Mathematics and Philosophy, Stanford University
Stanford, CA 94305
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. The Dialectica interpretation of arithmetic . . . . . . . . . . . . . . . . . . . . . 5
3. Consequences and benefits of the interpretation . . . . . . . . . . . . . . . . . . 15
4. Models of T , type structures, and normalizability . . . . . . . . . . . . . . . . . 20
5. The interpretation of fragments of arithmetic . . . . . . . . . . . . . . . . . . . 26
6. The interpretation of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7. Conservation results for weak K¨onig's lemma . . . . . . . . . . . . . . . . . . . 35
8. Non-constructive interpretations and applications . . . . . . . . . . . . . . . . . 41
9. The interpretation of theories of ordinals . . . . . . . . . . . . . . . . . . . . . . 50
10.Interpretations based on polymorphism . . . . . . . . . . . . . . . . . . . . . . 57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University
Feferman, Solomon - Departments of Philosophy & Mathematics, Stanford University

Collections: Mathematics; Multidisciplinary Databases and Resources