The Ground Axiom (GA)
| dc.creator | Reitz, Jonas | |
| dc.date | 2006-09-10 | |
| dc.date | 2007-02-21 | |
| dc.date.accessioned | 2026-07-07T07:47:47Z | |
| dc.date.available | 2026-07-07T07:47:47Z | |
| dc.description | A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set forcing extension of a model satisfying the Ground Axiom, is also first-order expressible, and its negation is consistent. | |
| dc.description | 25 pages; v2: corrected typos, removed some standard arguments from proofs | |
| dc.identifier | https://arxiv.org/abs/math/0609270 | |
| dc.identifier | http://arxiv.org/abs/math/0609270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124286 | |
| dc.subject | Logic | |
| dc.subject | 03E35 | |
| dc.title | The Ground Axiom (GA) | |
| dc.type | text |