# Mathematical Logic, Podnieks'page ...

Hi George, Stephen, Kory, & All.

I am thinking hard finding to find a reasonable way to explain the
technical part of the thesis, without being  ... too much technical.
The field of logic is rather hard to explain, without being
a little bit long and boring in the beginning :(

At least I found a very good Mathematical Logic Web page:
http://www.ltn.lv/~podnieks/index.html

The page contains also a test to see if you are platonist (actually it tests
only if you are an arithmetical realist!). Try it!

From that page I will be able to mention easily set of axioms, and rules.

For example below are the non logical axioms of Peano Arithmetic.
Does it makes intuitive sense ?

I suggest you try to find the logical axioms and the inference rules in
Podnieks page. This will define a precise exemple of loebian machine,
exactly those I will interview about the geometry of their
maximal consistent extensions (their comp histories) to see if it looks
like quantum logic as comp predict.

AxP(x) should be read: For any (natural number) x we have P(x), for
example: Ax((x = 0) or not (x = 0)) is a intuitively true proposition.

==============
The specific (non-logical) axioms of the first order arithmetic:

x=x,
x=y -> y=x,
x=y -> (y=z -> x=z),
x=y -> x+1=y+1,
~(0=x+1),
x=y -> x+1=y+1,
x+0=x,
x+(y+1)=(x+y)+1,
x*0=0,
x*(y+1)=(x*y)+x,

+ the following infinite set of formula:

B(0) & Ax(B(x)->B(x+1))   ->   AxB(x),        where B is any formula.