On interpretability in theories containing arithmetic
نویسندگان
چکیده
منابع مشابه
Interpretability over Peano Arithmetic
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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Interpretations are a natural tool in comparing the strength of two theories. In this paper we give a brief introduction to the topic of interpretability and interpretability logics. We will focus on the, so far, unknown interpretability logic of PRA. One research technique will be treated. This technique can be best described as restricting the realizations in the arithmetical semantics. 1 Wha...
متن کاملLogicism, interpretability, and Knowledge of Arithmetic
A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are re...
متن کاملThe 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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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1972
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-76-2-131-137