COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Indestructible remarkable cardinals

## Indestructible remarkable cardinalsAdd to your list(s) Download to your calendar using vCal - Gitman, V (City University of New York)
- Friday 28 August 2015, 16:00-17:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Mathematical, Foundational and Computational Aspects of the Higher Infinite In 2000, Schindler introduced remarkable cardinals and showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of $L(mathbb R)$ is absolute for proper forcing. Remarkable cardinals can be thought of either as a miniature version of strong cardinals or as having aspects of generic supercompactness, but they are relatively low in the large cardinal hierarchy. They are downward absolute to $L$ and lie (consistency-wise) between the 1-iterable and 2-iterable cardinals of the $lpha$-iterable cardinals hierarchy (below Ramsey cardinals). I will discuss the indestructibility properties of remarkable cardinals, which are similar to those of strong cardinals. I will show that a remarkable cardinal $kappa$ can be made simultaneously indestructible by all $ltkappa$-closed $leqkappa$-distributive forcing and by all forcing of the form ${ m Add}(kappa, heta)*mathbb R$, where $mathbb R$ is forced to be $ltkappa$-closed and $leqkappa$-distributive. For this argument, I will introduce the notion of a remarkable Laver function and show that every remarkable cardinal has one. Although, the existence of Laver-like functions can be forced for most large cardinals, few, such as strong, supercompact, and extendible cardinals, have them outright. The established indestructibility can be used to show, for instance, that any consistent continuum pattern on the regular cardinals can be realized above a remarkable cardinal and that a remarkable cardinal need not be even weakly compact in ${ m HOD }$. This is joint work with Yong Cheng. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsThe Leadership Masterclass series Cambridge Review of International Affairs SciScreen Cambridge Wolfson College Humanities Society talks Vital Geographies - Department of Geography Switch Off Week## Other talksThe Most Influential Living Philosopher? Why does cardiac function deteriorate in heart failure and how does phosphodiesterase 5 inhibition help? Dynamical large deviations in glassy systems ADMM for Exploiting Structure in MPC Problems Hide and seek: medieval creatures on the manuscript page Radiocarbon as a carbon cycle tracer in the 21st century |