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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.".
- Back-and-forth_method wikiPageID "2033586".
- Back-and-forth_method wikiPageRevisionID "595398447".
- Back-and-forth_method hasPhotoCollection Back-and-forth_method.
- 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 type Abstraction100002137.
- Back-and-forth_method type Argument106648724.
- Back-and-forth_method type Communication100033020.
- Back-and-forth_method type Evidence106643408.
- Back-and-forth_method type Indication106797169.
- Back-and-forth_method type MathematicalProof106647864.
- Back-and-forth_method type MathematicalProofs.
- Back-and-forth_method type Proof106647614.
- 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 label "カントールの往復論法".
- Back-and-forth_method sameAs カントールの往復論法.
- Back-and-forth_method sameAs m.06gl83.
- Back-and-forth_method sameAs Q4839003.
- Back-and-forth_method sameAs Q4839003.
- Back-and-forth_method sameAs Back-and-forth_method.
- Back-and-forth_method wasDerivedFrom Back-and-forth_method?oldid=595398447.
- Back-and-forth_method isPrimaryTopicOf Back-and-forth_method.