Girish Mahajan (Editor)

End extension

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In model theory and set theory, which are disciplines within mathematics, a model B = B , F of some axiom system of set theory T in the language of set theory is an end extension of A = A , E , in symbols A end B , if

  • A is a substructure of B , and
  • b A whenever a A and b F a hold, i.e., no new elements are added by B to the elements of A .
  • The following is an equivalent definition of end extension: A is a substructure of B , and { b A : b E a } = { b B : b F a } for all a A .

    For example, B , is an end extension of A , if A and B are transitive sets, and A B .

    References

    End extension Wikipedia