Any advice on a book about axiom of choice?

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ughaibu
 
Reply Mon 29 Mar, 2010 09:12 pm
I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?
 
Krumple
 
Reply Mon 29 Mar, 2010 09:51 pm
@ughaibu,
ughaibu;145962 wrote:
I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?


If I were to give you a list of books, how would you go about deciding which one to read?
 
ughaibu
 
Reply Mon 29 Mar, 2010 09:53 pm
@Krumple,
Krumple;145983 wrote:
If I were to give you a list of books, how would you go about deciding which one to read?
A list wouldn't be "any in particular". If this thread results in a list of recommendations, with reasons, then I'll assess what has been written. Before then, I dont know the answer to your question.
 
amist
 
Reply Mon 29 Mar, 2010 10:02 pm
@ughaibu,
What do you mean by 'axiom of choice'?
 
ughaibu
 
Reply Mon 29 Mar, 2010 10:14 pm
@amist,
amist;145989 wrote:
What do you mean by 'axiom of choice'?
Here you go: The Axiom of Choice (Stanford Encyclopedia of Philosophy)
 
Pepijn Sweep
 
Reply Tue 30 Mar, 2010 03:12 am
@ughaibu,
ughaibu;145962 wrote:
I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

Choice of what ? Fruits in summer, elements to mix with gold; it all depend were you work with.
 
raidon04
 
Reply Tue 6 Apr, 2010 03:24 am
@ughaibu,
I covered The Axiom of Choice briefly whilst reading Kurt Godel and its indeed rather intellectually stimulating but warrants a high consistency of concentration. Whilst you could read the original material of Ernst Zermelo I would instead advice you to cover a more contemporary account which includes numerous hypothesis' by a collection of different Mathematicians.
I would personally recommend a read of: From Frege to Godel: A Source Book in Mathematical Logic, as it covers the Axiom of choice as well as many other fundamental mathematical theorems.
Also, Godel's: The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. The consistency of the axiom of ... - Google Books

I hope my advice suffices.
 
ughaibu
 
Reply Tue 6 Apr, 2010 06:29 am
@raidon04,
raidon04;148750 wrote:
I hope my advice suffices.
Thanks, I'll keep a note of your suggestions. For the moment, I've ordered this: Amazon.com: Axiom of Choice (Lecture Notes in Mathematics) (9783540309895): Horst Herrlich: Books
 
Twirlip
 
Reply Sat 10 Apr, 2010 12:48 pm
@ughaibu,
ughaibu;145962 wrote:
I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?

A good, non-technical history is Gregory H. Moore, Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Springer 1982). I know I enjoyed reading or skim-reading it, but I'm afraid I can't remember in detail what I thought of it. Also, it's out of print.

A more technical treatment, recently republished by Dover as a cheap paperback, is Thomas J. Jech, The Axiom of Choice, but I'm afraid I haven't read it.
The Axiom of Choice
 
TuringEquivalent
 
Reply Sat 10 Apr, 2010 02:21 pm
@Twirlip,
The axiom say there is a choice function F for a set X of non-empty sets s .
If X is finite, and the sets in X in finite, then There is an enumerable number of such F. Surely, such F exist, but the problem shift to uniqueness. Which one is it? On the other hand, for the sets in X that might be infinite. You can ` t enumerate it, so that can be a problem.

simple case:

X= { {0, 1}, { 2, 3}}

has 4 candidate for F. They are { (0, 2), ( 0, 3), ( 1, 2), (1, 3)}.

while X= { N, C}

N is the natural numbers,

and

C is the complex numbers.

if we say:

1. { (x, y) | x in N, y in C}

This would solve the problem of existence( but not uniqueness), but 1 commit us to infinite sets.

The statement of the problem largely suppose existence of infinite sets, so i think the axiom of choice is largely to do with uniqueness, and not existence. They are separate questions.
 
VideCorSpoon
 
Reply Sat 10 Apr, 2010 06:07 pm
@TuringEquivalent,
TuringEquivalent;150337 wrote:
The axiom say there is a choice function F for a set X of non-empty sets s .
If X is finite, and the sets in X in finite, then There is an enumerable number of such F. Surely, such F exist, but the problem shift to uniqueness. Which one is it? On the other hand, for the sets in X that might be infinite. You can ` t enumerate it, so that can be a problem.

simple case:

X= { {0, 1}, { 2, 3}}

has 4 candidate for F. They are { (0, 2), ( 0, 3), ( 1, 2), (1, 3)}.

while X= { N, C}

N is the natural numbers,

and

C is the complex numbers.

if we say:

1. { (x, y) | x in N, y in C}

This would solve the problem of existence( but not uniqueness), but 1 commit us to infinite sets.

The statement of the problem largely suppose existence of infinite sets, so i think the axiom of choice is largely to do with uniqueness, and not existence. They are separate questions.


Ughaibu may be asking for a book rather than an answer. What is the name of the book that you draw this information from so that Ugaibu can look into it?
 
TuringEquivalent
 
Reply Sat 10 Apr, 2010 06:28 pm
@VideCorSpoon,
VideCorSpoon;150389 wrote:
Ughaibu may be asking for a book rather than an answer. What is the name of the book that you draw this information from so that Ugaibu can look into it?


Which piece of information? I just look at wikipedia, the notion of a choice function. The domain, and co-domain. The difference between existence, and uniqueness which is common in mathematical proofs. I don ` t know any particular book.
 
ughaibu
 
Reply Sat 10 Apr, 2010 06:44 pm
@Twirlip,
Twirlip;150299 wrote:
A good, non-technical history is Gregory H. Moore, Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Springer 1982). I know I enjoyed reading or skim-reading it, but I'm afraid I can't remember in detail what I thought of it. Also, it's out of print
Thanks. Unfortunately it's priced in the fantasy range.
Zermelo's Axiom of Choice: Its Origins, Development, and Influence: Amazon.ca: G.H. Moore: Books
Twirlip;150299 wrote:
A more technical treatment, recently republished by Dover as a cheap paperback, is Thomas J. Jech, The Axiom of Choice, but I'm afraid I haven't read it.
The Axiom of Choice
I considered that and Amazon.com: The Axiom of Choice (Studies in Logic Series) (9781904987543): John L Bell: Books I suspect, none exactly meets my fussiness. Anyway, I'll report on the Herrlich book, after it arrives.
 
Arjuna
 
Reply Sat 10 Apr, 2010 07:05 pm
@ughaibu,
ughaibu;150397 wrote:
Thanks. Unfortunately it's priced in the fantasy range.
Zermelo's Axiom of Choice: Its Origins, Development, and Influence: Amazon.ca: G.H. Moore: Books
I considered that and Amazon.com: The Axiom of Choice (Studies in Logic Series) (9781904987543): John L Bell: Books I suspect, none exactly meets my fussiness. Anyway, I'll report on the Herrlich book, after it arrives.
I would appreciate your sharing your thoughts on it. In which section should I expect to see your post?

I know what you mean about finding the book you want and gasping at the price. I guess that's a case for libraries. You know... the building with the books made out of paper. Actually sometimes they'll buy books you recommend... as I recall.
 
TuringEquivalent
 
Reply Sat 10 Apr, 2010 07:12 pm
@Arjuna,
http://publish.uwo.ca/~jbell/CHOICE.pdf


Jech, T., The Axiom of Choice. Amsterdam, North-Holland, 1973.
Moore, G.H., Zermelo's Axiom of Choice: Its Origin, Development, and Influence. New York:
Springer-Verlag, 1982.
Rubin, H., and Rubin, J., Equivalents of the Axiom of Choice, II. Amsterdam: North-Holland,
1985.
 
ughaibu
 
Reply Sat 10 Apr, 2010 09:58 pm
@Arjuna,
Arjuna;150401 wrote:
I would appreciate your sharing your thoughts on it. In which section should I expect to see your post?
I'll post on this thread.
Arjuna;150401 wrote:
Actually sometimes they'll buy books you recommend... as I recall.
I will be very surprised if I can talk a Japanese library into buying an obscure maths book, written in english, but, maybe I'll give it a go.
 
Arjuna
 
Reply Sat 10 Apr, 2010 11:55 pm
@ughaibu,
ughaibu;150432 wrote:
I'll post on this thread.I will be very surprised if I can talk a Japanese library into buying an obscure maths book, written in english, but, maybe I'll give it a go.
Yes, expensive plus obscure... there's also university libraries... and contacting the author and asking where you could borrow one. Path of least resistance: check out the cheaper ones first.
 
TuringEquivalent
 
Reply Tue 13 Apr, 2010 05:30 am
@ughaibu,
ughaibu;145962 wrote:
I'm planning to buy a book about the axiom of choice. Would you recommend any in particular, and if so, why?


I label you as a 5 - Enneagram Type Five: The Investigator


Quote:
Being a Five means always needing to learn, to take in information about the world. A day without learning is like a day without 'sunshine.


Quote:

They believe that developing this niche is the best way that they can attain independence and confidence.

Thus, for their own security and self-esteem, Fives need to have at least one area in which they have a degree of expertise that will allow them to feel capable and connected with the world.


I always thought free will, & determinism is what you are fixed on. It seems you are trying to branch out to "axiom of choice". I wonder what would make you feel insecure, ughaibu.
 
ughaibu
 
Reply Tue 13 Apr, 2010 06:37 am
@TuringEquivalent,
TuringEquivalent;151292 wrote:
I always thought free will, & determinism is what you are fixed on.
Strange, what's your explanation for all my battles against JTB?
 
TuringEquivalent
 
Reply Tue 13 Apr, 2010 07:50 am
@ughaibu,
ughaibu;151306 wrote:
Strange, what's your explanation for all my battles against JTB?


Does this describe you?:


Quote:
INTPs are relatively easy-going and amenable to almost anything until their principles are violated, about which they may become outspoken and inflexible. They prefer to return, however, to a reserved albeit benign ambiance, not wishing to make spectacles of themselves.


source: INTP Profile


In any case, it seems your are insecure about something..
 
 

 
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