Steve Vickers is a theoretical computer scientist based in Birmingham (U.K.).
On topology via formal logic (locales, sober topological spaces, …):
Steve Vickers, The double powerlocale and exponentiation: a case study in geometric logic, Theory and Applications of Categories 12 (2004) pp. 372-422 (pdf)
Steve Vickers, Locales and toposes as spaces, Chapter 8 in Handbook of Spatial Logics (ed. Aiello, Pratt-Hartman, van Bentham), Springer, 2007, pp. 429-496.
Steve Vickers, Continuity and geometric logic, Journal of Applied Logic 12 (1) (2014), pages 14-27 (pdf)
Ming Ng, Steve Vickers, Point-free Construction of Real Exponentiation, Logical Methods in Computer Science, Volume 18, Issue 3 (August 2, 2022), (doi:10.46298/lmcs-18(3:15)2022, arXiv:2104.00162)
Steven Vickers, Generalized point-free spaces, pointwise [arXiv:2206.01113]
Ming Ng, Steven Vickers, A Point-Free Look at Ostrowski’s Theorem and Absolute Values (arXiv:2308.14758)
Steve Vickers, The Fundamental Theorem of Calculus point-free, with applications to exponentials and logarithms, (arXiv:2312.05228)
Maria E. Maietti, Steve Vickers, An induction principle for consequence in arithmetic universes, JPAA 216 (2012) pp.2049-2067. [doi:10.1016/j.jpaa.2012.02.040, pdf]
Steve Vickers, Sketches for arithmetic universes, arXiv:1608.0159 (2016) &lbrackarXiv:1608.01559]
Steve Vickers, Arithmetic universes and classifying toposes [arXiv:1701.04611]
On geometric logic internal to Grothendieck toposes:
Last revised on June 5, 2024 at 02:28:57. See the history of this page for a list of all contributions to it.