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...http
>>  
>> ://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/




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