Ground axiom

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

References

• 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 
• Reitz, Jonas (2007), "The ground axiom", Journal of Symbolic Logic 72 (4): 1299–1317, doi:10.2178/jsl/1203350787, ISSN 0022-4812, http://projecteuclid.org/getRecord?id=euclid.jsl/1203350787 
• Reitz, Jonas (2008). The Ground Axiom (Ph.D.). CUNY Graduate Center. arXiv:math/0609064.