Quantal sets over involutive quantales
In this talk I shall report on work in progress with my student Joel Zamora Ramos of the University of Sussex on extending earlier work with Mohammad Nawaz on quantal sets over right Gelfand quantales. In doing so, I shall survey briefly the link between local sets and sheaves on a locale, as it was developed by Higgs, and then by Fourman and Scott, from the Boolean-valued sets introduced by Scott as an alternative approach to proving the independence of the Continuum Hypothesis. At this stage, one can give a fairly final description of the concept of quantal set that emerges in the involutive case, with an indication of the way in which the concept of a sheaf is defined over locally Gelfand quantales. Interestingly, as well as the spectrum of a C*-algebra, these quantales include the quantales introduced by Resende in characterising the quantale of a discrete localic groupoid.
Areas of interest
Christopher J. Mulvey (Univ. of Sussex/Univ. of Cambridge, UK)
March 18, 2005