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  

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.



>                               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/-Hide quoted text -
>>> - Show quoted text -- Hide quoted text -
>> - Show quoted text -
> >


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