8 comments on “Ultimate L

  1. Very engaging explanation the Continuum Hypothesis and the recent work done in this area. Quite enjoyable, for this long-ago reformed physicist.

  2. Thanks for writing the article. Really very interesting. Years ago I received a BS in Operations Research. I recently got interested in Set Theory and Logic. Specifically, I wanted to be able to go through Godel’s Incompleteness Theorem. In any case I’m currently learning an undergrad book called “Notes on Set Theory” during my morning commute. Its very enjoyable ! I have 2 questions for you.
    1) Any feedback on what are the best texts to go through for the self-taught student ?
    2) What’s been the response to Ultimate L from the general mathematical community ?
    Thanks.

  3. Hi Joel – I’m delighted you enjoyed the article.

    1) I started learning logic from a text called “Logic for mathematicians” by Hamilton. It’s very good, but might depend on your level of mathematical experience. On set theory specifically, Halmos’ Naive set theory is a nice book. There’s a recent book called Roads to Infinity by Stillwell, which isn’t really a teach-yourself book, but does give a beautiful overview of several areas of logic.

    2) I think ther jury’s still out on that! Many mathematicians don’t tend to pay much attention to what’s going on at the logical foundations, so it will take time before any consensus is formed. Also – importantly – the key Ultimate L conjectures have not yet been proven…

  4. This is an impressive piece of mathematical exposition. The subject of large cardinals is of course very technical, but you do a good job of conveying the flavor.

    I had no idea Woodin has reversed his opinion on the Continuum Hypothesis.

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