Bruno: It will take quite a while for Mendelson, so I may ask again when I am "finished" or want to start something new. Ronald

On Sep 29, 12:47 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 28 Sep 2009, at 21:51, ronaldheld wrote: > > > > > My book has arrived. Perhaps in several months, I will be able to > > follow the symbolic arguments better? > > Nice. Now I feel some guild because for all books in logic, there > exists always a better book :) > > The books by Torkel Fraenkel are very good. Too, like Carnielli and > Epstein and the Boolos and Jeffrey series. > > As a unique book for a serious study, some remains the best, like > Mendelson for an introduction to mathematical logic (a branch of math > which study the formal or symbolical systems) and Hartley Rogers for a > serious introduction to recursion theory (alias theoretical computer > science; computability theory, uncomputability theory, ...). > > And the book by Boolos (1979, 1993) are basically the best > introduction to the G and G* logics of self-reference. (The AUDA main > tools). > > Smullyan wrote many chef-d'oeuvre. > > The deepest bible of the field is Davis 1965, > > DAVIS M. (ed.), 1965, The Undecidable, Raven Press, Hewlett, New York. > > with the original papers by Gödel, Turing, Kleene, Church, and the > most incredible Paper which anticipated everything up to now and > beyond ... (I could argue). > It exists in DOVER now! > > My october month is a bit charged, and I am slow down. I will come > back on the diagonalization, and the "mathematical > definition or approach to the notion of computation, and the relation > between physics and the (mathematically shaped) border of the > uncomputable, asap. > > Best, > > Bruno > > > > > > > Ronald > > > On Sep 19, 5:38 pm, ronaldheld <ronaldh...@gmail.com> wrote: > >> Thanks, Bruno. Mendelson is on its way to me. > >> Ronald > > >> On Sep 18, 10:10 am, Bruno Marchal <marc...@ulb.ac.be> wrote: > > >>> Hi Ronald, > > >>> Mendelson' book is an excellent book. > > >>> The many editions of Boolos and Jeffrey are very good, but the > >>> mathematical logic part is not really self-contained. I like very > >>> much > >>> also the book by Epstein and Carnielli, and Epstein alone wrote nice > >>> big books on both classical and non classical logics, but I do think > >>> that Mendelson is one of the best introduction to classical > >>> mathematical logic. It gives the standard detailed account on > >>> computability, and on Gödel and Löb theorems. > > >>> Note that the understanding of UDA does not rely on mathematical > >>> logic, just on the notion of universal machine, and Church thesis > >>> (which I am explaining currently). But the "formal theory" and the > >>> notion of Löbian Machine, relies on mathematical logic. Those matter > >>> are not well known beyond the circle of mathematical logicians. > >>> Gödel's theorem is frequently abused (that does not help). > > >>> This makes me think about the book by Torkel Franzèn, which are very > >>> nice. Excellent complement to Mendelson. > > >>> Google on "Torkel Franzèn inexhaustibility" and "Torkel Franzèn > >>> abuse > >>> Gödel". You can't miss them. > > >>> If and when I try to explain AUDA, I can say more. Mendelson does > >>> not > >>> introduce to modal logic, but the little book by Bools 1979 does it > >>> very well, before using it for the formal self-reference. > > >>> So for AUDA, ma suggestion, for serious studies, is: > > >>> 1) Mendelson > >>> 2) Boolos 1979 > > >>> Bruno > > >>> On 18 Sep 2009, at 15:14, ronaldheld wrote: > > >>>> Bruno: > >>>> It sounds as if the way to begin is with the latest Mendelson > >>>> book. > >>>> Ronald > > >>>> On Sep 18, 2:55 am, Bruno Marchal <marc...@ulb.ac.be> wrote: > >>>>> Hi Ronald, > > >>>>> You may ask Günther Greindl, who asked me references for the UDA > >>>>> and > >>>>> AUDA, and he put them on the list archive. > > >>>>> guenther.grei...@gmail.com > > >>>>> You can take a look on the references in my > >>>>> theses.http://iridia.ulb.ac.be/~marchal/lillethesis/these/node79.html#SECTIO > >>>>> ... > >>>>> ://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/7%20biblio > >>>>> %20gen... > > >>>>> An excellent introduction to mathematical logic is the book by > >>>>> Eliot > >>>>> Mendelson. Classical treatises on the self-reference logic are the > >>>>> book by Boolos 1979 (recently reedited), or the later version: > >>>>> Boolos > >>>>> 1993. The book by Smorynski is very good too, but those books > >>>>> presuppose knowledge of logic (Like explained in Mendelson). > > >>>>> Then all books, technical or recreative by Raymond Smullyan, are > >>>>> introduction to diagonalization, self-reference, Gödel and Tarski > >>>>> theorem, and they are quite excellent. Notably his little > >>>>> recreative > >>>>> (but not so easy apparently) introduction to the modal G system; > >>>>> "Forever Undecided". > > >>>>> Ask if you have a problem to find them, or if you search for other > >>>>> books. Logicians like to write book, and there are many of them. > >>>>> Original papers on the UDA and AUDA can be found on my web pages > >>>>> (http://iridia.ulb.ac.be/~marchal/ > >>>>> ). > > >>>>> Bruno > > >>>>> On 10 Sep 2009, at 21:48, ronaldheld wrote: > > >>>>>> I thought that I would start a thread to consolidate some of the > >>>>>> books > >>>>>> useful in following current and old threads. if people alos > >>>>>> want to > >>>>>> post key papers here, I do not see a problem with that.- Hide > >>>>>> quoted text - > > >>>>> - Show quoted text - > > >>>http://iridia.ulb.ac.be/~marchal/-Hidequoted text - > > >>> - Show quoted text -- Hide quoted text - > > >> - Show quoted text - > > http://iridia.ulb.ac.be/~marchal/- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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