Ground axiom

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In set theory, the ground axiom was introduced by Hamkins (2005) and Reitz (2007). It states that the universe is not a nontrivial set forcing extension of an inner model.


  • Hamkins, Joel David (2005), "The Ground Axiom", Oberwolfach Report, 55: 3160–3162
  • Hamkins, Joel David; Reitz, Jonas; Woodin, W. Hugh (2008), "The ground axiom is consistent with V ≠ HOD", Proceedings of the American Mathematical Society, 136 (8): 2943–2949, doi:10.1090/S0002-9939-08-09285-X, ISSN 0002-9939, MR 2399062
  • Reitz, Jonas (2007), "The ground axiom", Journal of Symbolic Logic, 72 (4): 1299–1317, doi:10.2178/jsl/1203350787, ISSN 0022-4812, MR 2371206
  • Jonas Reitz (2008). The Ground Axiom (Ph.D.). CUNY Graduate Center.