Nonstandardness and the bounded functional interpretation
نویسندگان
چکیده
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 extended with nonstandard elements, then the bounded functional interpretation can be seen as falling out from a functional interpretation of nonstandard number theory without intensional notions. The original bounded functional interpretation can be seen as the trace left behind by the new interpretation when one sees it restricted to the standard number theoretical setting. We also answer an open question regarding the conservativity of the transfer principle via-à-vis functional interpretations of nonstandard arithmetic.
منابع مشابه
Hybrid Functional Interpretations of Linear and Intuitionistic Logic
This article shows how different functional interpretations can be combined into what we term hybrid functional interpretations. These hybrid interpretations work on the setting of a multi-modal linear logic. Functional interpretations of intuitionistic logic can be combined via Girard’s embedding of intuitionistic logic into linear logic. We first show how to combine the usual Kreisel’s modifi...
متن کاملFactorization of the Shoenfield-like Bounded Functional Interpretation
We adapt Streicher and Kohlenbach’s proof of the factorization S = K D of the Shoenfield translation S in terms of Krivine’s negative translation K and the Gödel functional interpretation D, obtaining a proof of the factorization U = K B of Ferreira’s Shoenfield-like bounded functional interpretation U in terms of K and Ferreira and Oliva’s bounded functional interpretation B.
متن کاملThe bounded functional interpretation of the double negation shift
We prove that the (non-intuitionistic) law of the double negation shift has a bounded functional interpretation with bar recursive functionals of finite type. As an application, we show that full numerical comprehension is compatible with the uniformities introduced by the characteristic principles of the bounded functional interpretation for the
متن کاملA note on the monotone functional interpretation
We prove a result relating the author’s monotone functional interpretation to the bounded functional interpretation due to Ferreira and Oliva. More precisely we show that (over model of majorizable functionals) largely a solution for the bounded interpretation also is a solution for monotone functional interpretation although the latter uses the existence of an underlying precise witness. This ...
متن کاملON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS
In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 166 شماره
صفحات -
تاریخ انتشار 2015