Thanks, Bruno. Mendelson is on its way to me.
Ronald
On Sep 18, 10:10 am, Bruno Marchal <marc....domain.name.hidden> 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 Franzčn, which are very
> nice. Excellent complement to Mendelson.
>
> Google on "Torkel Franzčn inexhaustibility" and "Torkel Franzčn 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....domain.name.hidden> 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....domain.name.hidden
>
> >> 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/- Hide quoted text -
>
> - Show quoted text -
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Received on Sat Sep 19 2009 - 14:38:01 PDT