Inner model theory: Difference between revisions
Jump to navigation
Jump to search
Content added Content deleted
RhubarbJayde (talk | contribs) (Created page with "Inner model theory is the study of the "fine structure theory" and construction of inner models, proper class-sized models of ZFC which satisfy the existence of large cardinals, covering, the generalized continuum hypothesis, and more. The smallest inner model is \(L\), which arguably has the most and the most detailed fine structure, but it is unable to accomodate measurable cardinals, in the sense that no cardinal, even if it really...") |
RhubarbJayde (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
Inner model theory is the study of the "fine structure theory" and construction of inner models, [[proper class]]-sized models of ZFC which satisfy the existence of large cardinals, covering, the generalized continuum hypothesis, and more. The smallest inner model is [[Constructible hierarchy|\(L\)]], which arguably has the most and the most detailed fine structure, but it is unable to |
Inner model theory is the study of the "fine structure theory" and construction of inner models, [[proper class]]-sized models of ZFC which satisfy the existence of large cardinals, covering, the generalized continuum hypothesis, and more. The smallest inner model is [[Constructible hierarchy|\(L\)]], which arguably has the most and the most detailed fine structure, but it is unable to accommodate [[measurable]] cardinals, in the sense that no cardinal, even if it really is measurable, is measurable in \(L\), and thus one needs to find inner models larger than \(L\). |
||
Inner model theory has given rise to the study of [[Sharp|sharps]], and many new [[Large cardinal|large cardinal axioms]] were developed for the purpose of inner model theory. |
Inner model theory has given rise to the study of [[Sharp|sharps]], and many new [[Large cardinal|large cardinal axioms]] were developed for the purpose of inner model theory. |
||
Latest revision as of 13:30, 1 September 2023
Inner model theory is the study of the "fine structure theory" and construction of inner models, proper class-sized models of ZFC which satisfy the existence of large cardinals, covering, the generalized continuum hypothesis, and more. The smallest inner model is \(L\), which arguably has the most and the most detailed fine structure, but it is unable to accommodate measurable cardinals, in the sense that no cardinal, even if it really is measurable, is measurable in \(L\), and thus one needs to find inner models larger than \(L\).
Inner model theory has given rise to the study of sharps, and many new large cardinal axioms were developed for the purpose of inner model theory.