Bounded functional interpretation
نویسندگان
چکیده
منابع مشابه
Bounded functional interpretation
We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Gödel’s functional “Dialectica” interpretation, the new interpretation does not care for precise witnesses of existential statements, but only for bounds for them. New principles are supported by our interpretation, including (a version of) the FAN theorem, weak König’s lemma and the lesser lim...
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The bounded functional interpretation of arithmetic in all finite types is able to interpret principles like weak König’s lemma without the need of any form of bar recursion. This interpretation requires the use of intensional (rule-governed) majorizability relations. This is a somewhat unusual feature. The main purpose of this paper is to show that if the base domain of the natural numbers is ...
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In this article we study applications of the bounded functional interpretation to theories of feasible arithmetic and analysis. The main results show that the novel interpretation is sound for considerable generalizations of weak König’s lemma, even in the presence of very weak induction. Moreover, when combined with Cook and Urquhart’s variant of the functional interpretation, one obtains effe...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2004.11.001