The interpretability logic of Peano arithmetic
نویسندگان
چکیده
منابع مشابه
The Interpretability Logic of Peano Arithmetic
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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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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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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It is known that PA(Q2), Peano arithmetic in a language with the Ramsey quantifier, is complete and compact and that its first-order consequences are the same as those of nj-CA0. A logic JFSiï^, called hyper-Ramsey logic, is defined; it is the union of an increasing sequence 3tf9lx Q JH^j Q JfOX^ Q ■ ■ ■ of sublogics, and ¿fa?, contains L(Q2). It is proved that VA(3?St„), which is Peano arithme...
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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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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 1990
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2274474