Core model: Difference between revisions

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In [[set theory]], the '''core model''' is a definable [[inner model]] of the [[von Neumann universe|universe]] of all [[Set (mathematics)|sets]]. Even though set theorists refer to "the core model", it is not a uniquely identified mathematical object. Rather, it is a class of inner models that under the right set-theoretic assumptions have very special properties, most notably [[covering lemma|covering properties]]. Intuitively, the core model is "the largest canonical inner model there is",<ref>{{cite (Ernest Schimmerling and [[John RarXiv|eprint=https://arxiv. Steel]])org/abs/math/9702206v1}}</ref> and is typically associated with a [[large cardinal]] notion. If Φ is a large cardinal notion, then the phrase "core model below Φ" refers to the definable inner model that exhibits the special properties under the assumption that there does ''not'' exist a cardinal satisfying Φ. The '''core model program''' seeks to analyze large cardinal axioms by determining the core models below them.

==History==