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Reverse mathematics

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axioms. It can be conceptualized as…

General principles, The big five subsystems of second-order arithmetic & Additional systems

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Overview

General principles

The big five subsystems of second-order arithmetic

Additional systems

Constructive reverse mathematics

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Reverse mathematics

Nodes109
Edges108
Triples42
Avg. degree1.98
Density0.018349
Components1

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Reverse mathematics

Top relations

related to Use of higher-order arithmetic · 10
Reverse mathematics → Cantor, Due, For, Higher-order, In, RCA0, RCAω, Such, The, Ulrich Kohlenbach
related to Constructive reverse mathematics · 7
Reverse mathematics → BISH, Bishop-style, CLASS, Constructive, INT, It, RUSS
related to Use of second-order arithmetic · 6
Reverse mathematics → Cauchy, For, In, Most, Such, The
related to General principles · 5
Reverse mathematics → Every, For, In, The, To
related to The big five subsystems of second-order arithmetic · 5
Reverse mathematics → Many, Polish, Reverse, Second-order, This
related to External links · 3
Reverse mathematics → Mathematics Zoo, Simpson's, Stephen
is a · 2
Reverse mathematics → program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics, program which is applied to constructive mathematics

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Important terminology

arithmetic second-order rca0 mathematics theorem countable reverse set axiom displaystyle theorems system theory induction scheme every comprehension weak arithmetical aca0

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Reverse mathematicsis aprogram in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics0.90text
Reverse mathematicsis aprogram which is applied to constructive mathematics0.90text
the classical theorem that the axiom of choiceinstance ofIt can be conceptualized as sculpting out necessary conditions from sufficient ones.The reverse mathematics program was foreshadowed by results in set theory0.80text
Zorn's lemma are equivalent over ZF set theoryinstance ofIt can be conceptualized as sculpting out necessary conditions from sufficient ones.The reverse mathematics program was foreshadowed by results in set theory0.80text
Post's theorem establish a close link between the complexity of a formulainstance ofresults0.80text
theinstance ofresults0.80text
Reverse mathematicsrelated to Constructive reverse mathematicsConstructive0.60section
Reverse mathematicsrelated to Constructive reverse mathematicsIt0.60section
Reverse mathematicsrelated to Constructive reverse mathematicsBISH0.60section
Reverse mathematicsrelated to Constructive reverse mathematicsBishop-style0.60section
Reverse mathematicsrelated to Constructive reverse mathematicsCLASS0.60section
Reverse mathematicsrelated to Constructive reverse mathematicsINT0.60section

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