nLab Steve Vickers

Steve Vickers is a theoretical computer scientist based in Birmingham (U.K.).

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Writings

On topology via formal logic (locales, sober topological spaces, …):

• Topology via Logic, Cambridge University Press (1989) (toc pdf)

On point-free topology:

• 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)

On arithmetic pretoposes:

• 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:

• Steven Vickers, Continuity and geometric logic, Journal of Applied Logic Volume 12, Issue 1, March 2014, Pages 14-27 (doi:10.1016/j.jal.2013.07.004)

Talks

• Steve Vickers, The Fundamental Theorem of Calculus: point-free, talk at the Topos Institute Colloquium, 30 May 2024 (video, slides)

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