A generalization of the Second Incompleteness Theorem and some exceptions to it
نویسندگان
چکیده
منابع مشابه
A generalization of the Second Incompleteness Theorem and some exceptions to it
This paper will introduce the notion of a naming convention and use this paradigm to both develop a new version of the Second Incompleteness Theorem and to describe when an axiom system can partially evade the Second Incompleteness Theorem.
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The Second Incompleteness Theorem states that axiom systems of sufficient strength are unable to verify their own consistency. Part of the reason that Gödel's theorem has fascinated logicians is that it almost defies common sense. This is because when human beings cogitate, they implicitly presume that thinking is a useful process. However, this tacit assumption would initially appear to presum...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2006
ISSN: 0168-0072
DOI: 10.1016/j.apal.2005.12.010