I’ve recently gotten into the habit of condensings readings I do in the course of research down to a single page in a 9cm x 14cm notebook. I’ve decided to share these summaries and notes here, as a backup in case I loose my notebook. I’m transcribing them here exactly as in my notebook, abbreviations and all. I would be interested in hearing from you if ever you think I’ve completely missed the point of the paper.
The first paper in the series is:
Boris Kushner. “Markov’s Constructive Mathematical Analysis: The Expectations and the Results.” Mathematical Logic, 1990, pp. 53–58.
Provides a brief survey of results in constructive maths in Markov’s sense. Gives the fundamental views/principles of Markov’s school of constructivism (paragraph 2). Mentions results concerning: constructive real numbers & functions, the topology of the plane, differential eqs, compleixity theo., constructive functional anal., etc. Surprising is the failure of the intermediate value theorem. The author presents a softening of the school’s view as constructivism being the only valid maths & says it has its place amongst the other branches. The author finds the purely syntactic nature of constructive maths of particular interest.