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- Reverse_mathematics abstract "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. The reverse mathematics program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory.Reverse mathematics is usually carried out using subsystems of second-order arithmetic, where many of its definitions and methods are inspired by previous work in constructive analysis and proof theory. The use of second-order arithmetic also allows many techniques from recursion theory to be employed; many results in reverse mathematics have corresponding results in computable analysis.The program was founded by Harvey Friedman (1975, 1976). A standard reference for the subject is (Simpson 2009).".
- Reverse_mathematics wikiPageExternalLink sosoa.
- Reverse_mathematics wikiPageExternalLink ~friedman.
- Reverse_mathematics wikiPageExternalLink simpson.
- Reverse_mathematics wikiPageID "326365".
- Reverse_mathematics wikiPageLength "26197".
- Reverse_mathematics wikiPageOutDegree "81".
- Reverse_mathematics wikiPageRevisionID "672097662".
- Reverse_mathematics wikiPageWikiLink Algebraic_closure.
- Reverse_mathematics wikiPageWikiLink Algorithmically_random_sequence.
- Reverse_mathematics wikiPageWikiLink Analytical_hierarchy.
- Reverse_mathematics wikiPageWikiLink Archimedean_property.
- Reverse_mathematics wikiPageWikiLink Arithmetical_hierarchy.
- Reverse_mathematics wikiPageWikiLink Arzelà–Ascoli_theorem.
- Reverse_mathematics wikiPageWikiLink Ascolis_theorem.
- Reverse_mathematics wikiPageWikiLink Axiom.
- Reverse_mathematics wikiPageWikiLink Axiom_of_choice.
- Reverse_mathematics wikiPageWikiLink Axiom_schema.
- Reverse_mathematics wikiPageWikiLink Axiom_scheme.
- Reverse_mathematics wikiPageWikiLink Baire_category_theorem.
- Reverse_mathematics wikiPageWikiLink Baire_space.
- Reverse_mathematics wikiPageWikiLink Banach–Steinhaus_theorem.
- Reverse_mathematics wikiPageWikiLink Bolzano–Weierstrass_theorem.
- Reverse_mathematics wikiPageWikiLink Brouwer_fixed-point_theorem.
- Reverse_mathematics wikiPageWikiLink Brouwer_fixed_point_theorem.
- Reverse_mathematics wikiPageWikiLink Cambridge_University_Press.
- Reverse_mathematics wikiPageWikiLink Cantor–Bendixson_theorem.
- Reverse_mathematics wikiPageWikiLink Category:Computability_theory.
- Reverse_mathematics wikiPageWikiLink Category:Mathematical_logic.
- Reverse_mathematics wikiPageWikiLink Category:Proof_theory.
- Reverse_mathematics wikiPageWikiLink Cauchy_sequence.
- Reverse_mathematics wikiPageWikiLink Commutative_ring.
- Reverse_mathematics wikiPageWikiLink Complete_metric_space.
- Reverse_mathematics wikiPageWikiLink Computability_theory.
- Reverse_mathematics wikiPageWikiLink Computable_analysis.
- Reverse_mathematics wikiPageWikiLink Computable_function.
- Reverse_mathematics wikiPageWikiLink Constructive_analysis.
- Reverse_mathematics wikiPageWikiLink Constructivism_(mathematics).
- Reverse_mathematics wikiPageWikiLink Countable_set.
- Reverse_mathematics wikiPageWikiLink Determinacy.
- Reverse_mathematics wikiPageWikiLink Effective_Polish_space.
- Reverse_mathematics wikiPageWikiLink Elementary_function_arithmetic.
- Reverse_mathematics wikiPageWikiLink Epsilon_numbers_(mathematics).
- Reverse_mathematics wikiPageWikiLink Epsilon_zero.
- Reverse_mathematics wikiPageWikiLink Feferman–Schütte_ordinal.
- Reverse_mathematics wikiPageWikiLink Field_(mathematics).
- Reverse_mathematics wikiPageWikiLink Group_(mathematics).
- Reverse_mathematics wikiPageWikiLink Gxc3xb6dels_completeness_theorem.
- Reverse_mathematics wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Reverse_mathematics wikiPageWikiLink Hahn–Banach_theorem.
- Reverse_mathematics wikiPageWikiLink Height_(abelian_group).
- Reverse_mathematics wikiPageWikiLink Heine–Borel_theorem.
- Reverse_mathematics wikiPageWikiLink Impredicativity.
- Reverse_mathematics wikiPageWikiLink Infimum_and_supremum.
- Reverse_mathematics wikiPageWikiLink Intermediate_value_theorem.
- Reverse_mathematics wikiPageWikiLink Jordan_curve_theorem.
- Reverse_mathematics wikiPageWikiLink Kleenes_recursion_theorem.
- Reverse_mathematics wikiPageWikiLink Kxc3xb6nigs_lemma.
- Reverse_mathematics wikiPageWikiLink Low_(computability).
- Reverse_mathematics wikiPageWikiLink Low_basis_theorem.
- Reverse_mathematics wikiPageWikiLink Lusins_separation_theorem.
- Reverse_mathematics wikiPageWikiLink Mathematical_logic.
- Reverse_mathematics wikiPageWikiLink Maximal_ideal.
- Reverse_mathematics wikiPageWikiLink Metric_space.
- Reverse_mathematics wikiPageWikiLink Natural_number.
- Reverse_mathematics wikiPageWikiLink Nested_intervals.
- Reverse_mathematics wikiPageWikiLink Nested_sequence_of_closed_intervals.
- Reverse_mathematics wikiPageWikiLink Open_set.
- Reverse_mathematics wikiPageWikiLink Ordered_field.
- Reverse_mathematics wikiPageWikiLink Perfect_set_property.
- Reverse_mathematics wikiPageWikiLink Posts_theorem.
- Reverse_mathematics wikiPageWikiLink Prime_ideal.
- Reverse_mathematics wikiPageWikiLink Primitive_recursive_arithmetic.
- Reverse_mathematics wikiPageWikiLink Proof_theory.
- Reverse_mathematics wikiPageWikiLink Psi0(Omega_omega).
- Reverse_mathematics wikiPageWikiLink Rational_number.
- Reverse_mathematics wikiPageWikiLink Real_closed_field.
- Reverse_mathematics wikiPageWikiLink Real_number.
- Reverse_mathematics wikiPageWikiLink Recursion_theory.
- Reverse_mathematics wikiPageWikiLink Riemann_integral.
- Reverse_mathematics wikiPageWikiLink Ring_(mathematics).
- Reverse_mathematics wikiPageWikiLink Robinson_arithmetic.
- Reverse_mathematics wikiPageWikiLink Second-order_arithmetic.
- Reverse_mathematics wikiPageWikiLink Second_order_arithmetic.
- Reverse_mathematics wikiPageWikiLink Separable_space.
- Reverse_mathematics wikiPageWikiLink Supremum.
- Reverse_mathematics wikiPageWikiLink Theorem.
- Reverse_mathematics wikiPageWikiLink Transcendence_basis.
- Reverse_mathematics wikiPageWikiLink Transcendence_degree.
- Reverse_mathematics wikiPageWikiLink Ulms_theorem.
- Reverse_mathematics wikiPageWikiLink Uniform_boundedness_principle.
- Reverse_mathematics wikiPageWikiLink Vector_space.
- Reverse_mathematics wikiPageWikiLink Well-order.
- Reverse_mathematics wikiPageWikiLink Well_ordering.
- Reverse_mathematics wikiPageWikiLink ZF_set_theory.
- Reverse_mathematics wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Reverse_mathematics wikiPageWikiLink Zorns_lemma.
- Reverse_mathematics wikiPageWikiLink Ψ₀(Ωω).
- Reverse_mathematics wikiPageWikiLinkText "Reverse mathematics".
- Reverse_mathematics wikiPageWikiLinkText "Reverse_mathematics#Weak_K.C3.B6nig.27s_lemma_WKL0".