The ground axiom
Copyright policy )The ground axiom
AbstractA 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.
- City University of New York United States
- New York City College of Technology United States
- City University of New York United States
the Bedrock Axiom, coding, ordinal definability, the Ground Axiom, Mathematics - Logic, Other set-theoretic hypotheses and axioms, 03E35, Inner models, including constructibility, ordinal definability, and core models, forcing, FOS: Mathematics, Forcing, Consistency and independence results, Logic (math.LO)
the Bedrock Axiom, coding, ordinal definability, the Ground Axiom, Mathematics - Logic, Other set-theoretic hypotheses and axioms, 03E35, Inner models, including constructibility, ordinal definability, and core models, forcing, FOS: Mathematics, Forcing, Consistency and independence results, Logic (math.LO)
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