Caltrops - The Knuckle Shuffle

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by mark 02/20/2003, 11:52am PST

Chairman Mao wrote:

I need a text on mathematical logic;

When working though the set theory text I have right now I would like to be able to do the proofs myself. It shows all the proofs, but does not list the rules. Its been a very, very long time since I did any proofs. I want it for more than just that, since I'm going back to school for a _{physics degree} and am refreshing all the math that the black spot in my adolescent head swallowed the first time around. I know I'm using a bunch of terms incorrectly here. Its been a long, long time.

Do they provide any axioms or identities in there? Specifically I'm thinking Axiom of Choice, Rule of Replacement, etc. That set theory, I think, is called von Neumann-Bernays-GÃ¶del and looks a lot like first order logic. For that one, I'm not really sure what all the rules are. In a sort of simple, generic set theory, your core identities should look something like this:

(+ intersection, | union, E everything, N nullset, ~ complement)

Complementation Law
A | ~A = E

Exculsion Law
A + ~A = N

Indentity Laws
A + E = A
A | N = A

Domination
A | E = E
A + N = N

Idempotent Laws
A | A = A
A + A = A

Double complementation law
~(~A) = A

Communitive Laws
A | B = B | A
A + B = B + A

Associative Laws
(A | B) | C = A | (B | C)
(A + B) + C = A + (B + C)

Distributive Laws
A | (B + C) = (A | B) + (A | C)
A + (B | C) = (A + B) | (A + C)

De Morgan's laws
~(A + B) = ~A | ~B
~(A | B) = ~A + ~B

(From Logic and Discrete Mathematics by Grassman and Tremblay, which is a infuriating text in many many ways..)

If that doesn't help, get a book from the libarary on NGB or more complicated set theory that what I have provided. As far as "pure" first order logic goes, Modern Logic by Graeme Forbes seems pretty good, you can probably find that at a library too.

mark

Suggestions, please.. . by Chairman Mao 02/20/2003, 3:29am PST NEW

Set theory... by mark 02/20/2003, 11:52am PST NEW

That helps nicely, thank you -nt- NT by Chairman Mao 02/20/2003, 12:22pm PST NEW