منابع مشابه
Reverse-engineering Reverse Mathematics
An important open problem in Reverse Mathematics ([16, 25]) is the reduction of the first-order strength of the base theory from IΣ1 to I∆0 + exp. The system ERNA, a version of Nonstandard Analysis based on the system I∆0 + exp, provides a partial solution to this problem. Indeed, Weak König’s lemma and many of its equivalent formulations from Reverse Mathematics can be ‘pushed down’ into ERNA,...
متن کاملReverse Mathematics
In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can be shown that theorems from different fields of math such as group theory and analysis are in fact equivalen...
متن کاملReverse Reverse-Engineering
Reverse engineering a program constructs a high-level representation suitable for various software development purposes such as documentation or reengineering. Unfortunately however, there are no established guidelines to assess the adequacy of such a representation. We propose two such criteria, completeness and accuracy, and show how they can be determined during the course of reversing the r...
متن کاملReverse Engineering is Reverse Forward Engineering
Reverse Engineering is focused on the challenging task of understanding legacy program code without having suitable documentation. Using a transformational forward engineering perspective, we gain the insight that much of this difficulty is caused by design decisions made during system development. Such decisions “hide” the program functionality and performance requirements in the final system ...
متن کاملFinite Reverse Mathematics
We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic. 1. T0 and IS0. In this section, we introduce the system T0, and show that it corresponds to the...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.11.006