Woodin for strong compactness cardinals

We give the definition of Woodin for strong compactness cardinals, the Woodinised version of strong compactness, and we prove an analogue of Magidor's identity crisis theorem for the first strongly compact cardinal.Comment: 20 pages, fixed proof of Theorem 4.1, minor corrections and addition

City Designed for Subtropical Living - Carrying forward the momentum from Subtropical Cities 2006

At a time when cities around the world are increasingly looking and feeling the same, and similarly adding to mounting environmental crises, the Subtropical Cities conference hosted by the Centre for Subtropical Design in Brisbane a few months ago generated keen enthusiasm for ways subtropical environments can produce new models for urbanism and address the problems of the contemporary city. Subtropical Cities was characterised by a genuine sense of excitement about how, in the subtropics, we can plan and design urbanism that is enriched by commitment to local distinctiveness through attention to climate, cultural values and landscape. The conference confirmed that if we are to face the challenges of today and the future, we need a framework that accommodates complexity and diversity. Invaluable micro-tactics and subtle incremental changes which dwell on amenity and liveability are necessary; not the tallest, not the biggest, not the most spectacular! Such excesses are easily achieved

Superstrong and other large cardinals are never Laver indestructible

Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals, superstrongly unfoldable cardinals, \Sigma_n-reflecting cardinals, \Sigma_n-correct cardinals and \Sigma_n-extendible cardinals (all for n>2) are never Laver indestructible. In fact, all these large cardinal properties are superdestructible: if \kappa\ exhibits any of them, with corresponding target \theta, then in any forcing extension arising from nontrivial strategically <\kappa-closed forcing Q in V_\theta, the cardinal \kappa\ will exhibit none of the large cardinal properties with target \theta\ or larger.Comment: 19 pages. Commentary concerning this article can be made at http://jdh.hamkins.org/superstrong-never-indestructible. Minor changes in v