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- Extension_by_definitions abstract "In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol for the set which has no member. In the formal setting of first-order theories, this can be done by adding to the theory a new constant and the new axiom , meaning 'for all x, x is not a member of '. It can then be proved that doing so adds essentially nothing to the old theory, as should be expected from a definition. More precisely, the new theory is a conservative extension of the old one.".
- Extension_by_definitions wikiPageID "12219849".
- Extension_by_definitions wikiPageRevisionID "454088873".
- Extension_by_definitions hasPhotoCollection Extension_by_definitions.
- Extension_by_definitions subject Category:Mathematical_logic.
- Extension_by_definitions subject Category:Proof_theory.
- Extension_by_definitions comment "In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol for the set which has no member. In the formal setting of first-order theories, this can be done by adding to the theory a new constant and the new axiom , meaning 'for all x, x is not a member of '.".
- Extension_by_definitions label "Extension by definitions".
- Extension_by_definitions sameAs m.02vw9zn.
- Extension_by_definitions sameAs Q5421941.
- Extension_by_definitions sameAs Q5421941.
- Extension_by_definitions wasDerivedFrom Extension_by_definitions?oldid=454088873.
- Extension_by_definitions isPrimaryTopicOf Extension_by_definitions.