books on logic/computing

[ronaldheld]

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.

[Bruno Marchal]

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...@gmail.com

You can take a look on the references in my theses.
http://iridia.ulb.ac.be/~marchal/lillethesis/these/node79.html#SECTION001300000000000000000
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/7%20biblio%20generale.pdf

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

[ronaldheld]

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 -

[Bruno Marchal]

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

http://iridia.ulb.ac.be/~marchal/

[ronaldheld]

Thanks, Bruno. Mendelson is on its way to me.
Ronald

> >> ://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 -

[ronaldheld]

My book has arrived. Perhaps in several months, I will be able to
follow the symbolic arguments better?
Ronald

> >http://iridia.ulb.ac.be/~marchal/-Hide quoted text -
>
> > - Show quoted text -- Hide quoted text -

[Bruno Marchal]

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

http://iridia.ulb.ac.be/~marchal/

[ronaldheld]

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

> >>>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 -