Interpretability suprema in Peano Arithmetic
نویسندگان
چکیده
منابع مشابه
Interpretability suprema in Peano Arithmetic
This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic ILM of Peano Arithmetic (PA). It is wellknown that any theories extending PA have a supremum in the interpretability ordering. While provable in PA, this fact is not reflected in the theorems of the modal system ILM, due to limited expressive power. Our goal is to enrich the lan...
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We investigate the modal logic of interpretability over Peano arith metic PA Our main result is an extension of the arithmetical complete ness theorem for the interpretability logic ILM This extension concerns recursively enumerable sets of formulas of interpretability logic rather than single formulas As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability...
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PA is Peano arithmetic. The formula InterppA(r,/l) is a formalization of the assertion that the theory PA + a interprets the theory PA + , O (the variables a and are intended to range over codes of sentences of PA). We extend Solovay's modal analysis of the formalized provability predicate of PA, PrpA(x), to the case of the formalized interpretability relation Interp,,(x, y). The relevant modal...
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The project is designed for an upper level undergraduate course in mathematical logic. Although the project is relatively short, some of the exercises are not as easy as they appear. Instructors may wish to spend some class time on discussing how formal proofs should be conducted, and also provide some additional assistance with completing some of the exercises. The last part of the project ass...
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Let sf be a structure and let U be a subset of \sf\. We say U is extendible if whenever 3S is an elementary extension of so? .there is a V Ç \£§\ such that (sf, U) -< (SS, V). Our main results are: If Jt is a countable model of Peano arithmetic and U is a subset of |-#|, then U is extendible iff U is parametrically definable in J( . Also, the cofinally extendible subsets of \J?\ are exactly the...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2017
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-017-0557-4