Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Godel's Functional ("Dialectica") Interpretation Jeremy Avigad
 

Summary: CHAPTER VI
GĻodel'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 KĻonig'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