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...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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Received on Fri Sep 18 2009 - 16:10:28 PDT