Reverse Mathematics
نویسندگان
چکیده
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,...
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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...
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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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This paper develops the Reverse Mathematics of second countable topologies, where the elements of the topological space exist. The notion of topology, effective topology (Dorais 2011), and basis will be defined. Several concepts and results that appear in the practice of general topology will be developed in various subsystems of second order arithmetic, Z2. Several of the ideas and results of ...
متن کاملReverse Mathematics of Matroids
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2018
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1732