I always had the dream to design a course for my graduate students like "mathematical models of the continuum". This course should cover history of real numbers, the Measure Problem, the Banach-Tarski Paradox, but also Baire/Cantor/Polish spaces, and it should look at infinite games and determinacy as well.


Obviously I am conscious about the text books and articles covering all these concepts. However, I seem to be unable to find a rigorours, graduate-level monograph that captures all of this in one, which I could potentially use as a text.


Would someone be able to point me to a good reference for that?



Reference for graduate-level text or monograph with focus on "the continuum"
I like your idea of such a course a lot! If it is appropriate to recommend a book in German language, I think this one could be the perfect match:


Oliver Deiser (2007): *Reelle Zahlen: Das klassische Kontinuum und die natürlichen Folgen*


I own this book and can say it covers all the topics that you mentioned, and it is certainly a graduate-level text. I find the quality of the exposition outstanding, and the range of topics quite unique. It covers the historical development quite extensively and gives many references, with a focus on the original sources.


I think there is also a 2nd edition from 2008.


