Yes, that’s beautiful work. Quite advanced, though. The wonderful world of ZFC + Determinacy.
But most people have already difficulties for the extremely simple first order arithmetic of for the combinatory algebra, so set theory, … well, my student asks me to do a little bit of it, and I took pleasure explains the behavior of the Goodstein sequences, which motivates in arithmetic for using transfinite induction. It might take month of work to get that paper right, so I will stay mute on its relation with Indexical Digital Mechanism, at least for some period. But it is excellent theology! I have thousand of extraordinary paper on arithmetical and set-theoretical self-reference, it is a blooming subject, even if sometimes, the fashion carried a bit away, but it always comes back, and self-reference is where mathematical logic taught the most fascinating discovery, to begin with Gödel 1931. Bruno > On 5 Jun 2019, at 12:21, Philip Thrift <[email protected]> wrote: > > > Computational self-reference and the universal algorithm > Queen Mary University of London, June 2019 > > via @JDHamkins > > This was a talk for the Theory Seminar for the theory research group in > Theoretical Computer Science at Queen Mary University of London. The talk was > held 4 June 2019 1:00 pm. > > > Abstract. Curious, often paradoxical instances of self-reference inhabit deep > parts of computability theory, from the intriguing Quine programs and > Ouroboros programs to more profound features of the Gödel phenomenon. In this > talk, I shall give an elementary account of the universal algorithm, showing > how the capacity for self-reference in arithmetic gives rise to a Turing > machine program e, which provably enumerates a finite set of numbers, but > which can in principle enumerate any finite set of numbers, when it is run in > a suitable model of arithmetic. In this sense, every function becomes > computable, computed all by the same universal program, if only it is run in > the right world. Furthermore, the universal algorithm can successively > enumerate any desired extension of the sequence, when run in a suitable > top-extension of the universe. An analogous result holds in set theory, where > Woodin and I have provided a universal locally definable finite set, which > can in principle be any finite set, in the right universe, and which can > furthermore be successively extended to become any desired finite superset of > that set in a suitable top-extension of that universe. > > http://jdh.hamkins.org/computational-self-reference-and-the-universal-algorithm-queen-mary-university-of-london-june-2019/ > slides: > http://jdh.hamkins.org/wp-content/uploads/Computational-self-reference-and-the-universal-algorithm-QMUL-2019-1.pdf > > > @philipthrift > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/aff13ede-4051-4509-aa52-4a9a1484dd31%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/aff13ede-4051-4509-aa52-4a9a1484dd31%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/DE483CF8-1A76-4CDB-9D49-8B0177DB7F72%40ulb.ac.be.
