|
gptkbp:instanceOf
|
field of mathematical logic
|
|
gptkbp:aims_to_determine
|
minimal axioms needed to prove theorems
|
|
gptkbp:analyzes
|
theorems of mathematics
|
|
gptkbp:appliesTo
|
gptkb:classical_mathematics
gptkb:algebra
gptkb:set_theory
analysis
combinatorics
|
|
gptkbp:central_question
|
which axioms are required to prove a given theorem
|
|
gptkbp:developedBy
|
gptkb:Harvey_Friedman
|
|
gptkbp:focusesOn
|
subsystems of second-order arithmetic
|
|
gptkbp:further_developed_by
|
gptkb:Stephen_Simpson
|
|
gptkbp:has_five_main_subsystems
|
gptkb:Π^1_1-CA_0
gptkb:ATR_0
ACA_0
RCA_0
WKL_0
|
|
gptkbp:has_main_result
|
many theorems are equivalent to one of the five subsystems
|
|
gptkbp:hasApplication
|
analyzing independence results
classifying mathematical statements
mathematical logic education
understanding logical strength of theorems
|
|
gptkbp:hasConcept
|
equivalence of theorems and axioms
|
|
gptkbp:hasMethod
|
reversing theorems to axioms
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Reverse mathematics
|
|
gptkbp:main_framework
|
gptkb:second-order_arithmetic
|
|
gptkbp:notableContributor
|
gptkb:Stephen_G._Simpson
|
|
gptkbp:publishedIn
|
gptkb:Subsystems_of_Second_Order_Arithmetic
|
|
gptkbp:relatedTo
|
computability theory
foundations of mathematics
proof theory
|
|
gptkbp:studies
|
gptkb:axiomatic_foundations_of_mathematics
|
|
gptkbp:studies_equivalence_over
|
RCA_0
|
|
gptkbp:uses_base_system
|
RCA_0
|
|
gptkbp:bfsParent
|
gptkb:The_foundations_of_mathematics
|
|
gptkbp:bfsLayer
|
7
|