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- Back-and-forth_method abstract "In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular: It can be used to prove that any two countably infinite densely ordered sets (i.e., linearly ordered in such a way that between any two members there is another) without endpoints are isomorphic. An isomorphism between linear orders is simply a strictly increasing bijection. This result implies, for example, that there exists a strictly increasing bijection between the set of all rational numbers and the set of all real algebraic numbers. It can be used to prove that any two countably infinite atomless Boolean algebras are isomorphic to each other. It can be used to prove that any two equivalent countable atomic models of a theory are isomorphic. It can be used to prove that the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, always produces a unique graph, the Rado graph. It can be used to prove that any two m-complete r.e. sets are recursively isomorphic.".
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- Back-and-forth_method wikiPageLength "5421".
- Back-and-forth_method wikiPageOutDegree "33".
- Back-and-forth_method wikiPageRevisionID "688243628".
- Back-and-forth_method wikiPageWikiLink Algebraic_number.
- Back-and-forth_method wikiPageWikiLink Atomic_model_(mathematical_logic).
- Back-and-forth_method wikiPageWikiLink Bertrand_Russell.
- Back-and-forth_method wikiPageWikiLink Bijection.
- Back-and-forth_method wikiPageWikiLink Boolean_algebra_(structure).
- Back-and-forth_method wikiPageWikiLink Cambridge_University_Press.
- Back-and-forth_method wikiPageWikiLink Category:Articles_containing_proofs.
- Back-and-forth_method wikiPageWikiLink Category:Mathematical_proofs.
- Back-and-forth_method wikiPageWikiLink Category:Model_theory.
- Back-and-forth_method wikiPageWikiLink Cooper_Harold_Langford.
- Back-and-forth_method wikiPageWikiLink Countable_set.
- Back-and-forth_method wikiPageWikiLink Dense_order.
- Back-and-forth_method wikiPageWikiLink Ehrenfeucht–Fraïssé_game.
- Back-and-forth_method wikiPageWikiLink Erdős–Rényi_model.
- Back-and-forth_method wikiPageWikiLink Georg_Cantor.
- Back-and-forth_method wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Back-and-forth_method wikiPageWikiLink Harvard_University_Press.
- Back-and-forth_method wikiPageWikiLink Isomorphism.
- Back-and-forth_method wikiPageWikiLink Many-one_reduction.
- Back-and-forth_method wikiPageWikiLink Mathematical_logic.
- Back-and-forth_method wikiPageWikiLink Model_theory.
- Back-and-forth_method wikiPageWikiLink Rado_graph.
- Back-and-forth_method wikiPageWikiLink Random_graph.
- Back-and-forth_method wikiPageWikiLink Rational_number.
- Back-and-forth_method wikiPageWikiLink Re.
- Back-and-forth_method wikiPageWikiLink Real_number.
- Back-and-forth_method wikiPageWikiLink Recursive_function.
- Back-and-forth_method wikiPageWikiLink Roland_Fraïssé.
- Back-and-forth_method wikiPageWikiLink Set_theory.
- Back-and-forth_method wikiPageWikiLink Springer_Science+Business_Media.
- Back-and-forth_method wikiPageWikiLink Total_order.
- Back-and-forth_method wikiPageWikiLinkText "Back-and-forth method".
- Back-and-forth_method wikiPageWikiLinkText "back-and-forth method".
- Back-and-forth_method wikiPageUsesTemplate Template:Citation.
- Back-and-forth_method wikiPageUsesTemplate Template:Disambiguation_needed.
- Back-and-forth_method subject Category:Articles_containing_proofs.
- Back-and-forth_method subject Category:Mathematical_proofs.
- Back-and-forth_method subject Category:Model_theory.
- Back-and-forth_method hypernym Method.
- Back-and-forth_method type Software.
- Back-and-forth_method type Proof.
- Back-and-forth_method type Theorem.
- Back-and-forth_method comment "In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular: It can be used to prove that any two countably infinite densely ordered sets (i.e., linearly ordered in such a way that between any two members there is another) without endpoints are isomorphic. An isomorphism between linear orders is simply a strictly increasing bijection.".
- Back-and-forth_method label "Back-and-forth method".
- Back-and-forth_method sameAs Q4839003.
- Back-and-forth_method sameAs カントールの往復論法.
- Back-and-forth_method sameAs Método_vai-e-volta.
- Back-and-forth_method sameAs m.06gl83.
- Back-and-forth_method sameAs Q4839003.
- Back-and-forth_method wasDerivedFrom Back-and-forth_method?oldid=688243628.
- Back-and-forth_method isPrimaryTopicOf Back-and-forth_method.