Re: Request for Reference/Link to example of defining a theory/logic.
- From: "Charlie-Boo" <shymathguy@xxxxxxxxx>
- Date: 9 Nov 2006 17:08:21 -0800
Scott wrote:
Hi:
I am requesting help in locating a link or reference showing an example
of defining a theory and/or logic. I am constructing a formal system
that will emulate first-order logic and set theory.
Why?
Many people would say "Which set theory?" (but not I - I know there is
only one true set theory.)
I am unsure what is
the minimum theorem/proofs necessary to demonstrate that the formal
system does indeed include first-order logic and set theory.
With the above approach, choose a set theory and just make sure you can
prove its axioms.
Or even better, show a much simpler representation of the axioms than
using klunky Predicate Calculus. Let M#P(x) for any expression P()
mean that set M contains exactly the elements of P. Let P(x) mean
there is such an M, and -P(x) mean there is not. And SE(a,b) means (b
e a). Then e.g. the axiom of the empty set is ~TRUE(x). The axiom of
regularity (what it's trying to do) is -~SE(x,x). The rest of the ZF
et. al. axoims are easily represented in a much simpler, clearer
notation than usual.
Or even better yet, insted of reinventing the wheel, invent a new
wheel: axiomatize some branch of Computer Science, e.g. Theory of
Computation (Turing), Recursion Theory (Kleene), Program Synthesis
(Boo), Incompleteness in Logic (Godel) etc. Or a branch of Mathematics
e.g. Number Theory (Peano Arithmetic is terrible for this - just as bad
as ZF.)
C-B
Does
anyone know of a web reference or book that dwelves into this topic?
Thanks.
Regards,
Scott
.
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