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Logical problems of functional interpretations

✍ Scribed by Justus Diller

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 135 KB
Volume: 114
Category: Article
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(01)00074-4

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✦ Synopsis

G odel interpreted Heyting arithmetic HA in a "logic-free" fragment T0 of his theory T of primitive recursive functionals of ÿnite types by his famous Dialectica-translation D . This works because the logic of HA is extremely simple. If the logic of the interpreted system is di erent-in particular more complicated-, it forces us to look for di erent and more complicated functional translations. We discuss the arising logical problems for arithmetical and set theoretical systems from HA to CZF. We want to test the thesis: While the functionals take care of the proof theoretic strength of the interpreted system, it is the functional translation that has to cope with the logical complexities of the system.

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