[FOM] A simplification of Structure Theory.

[Zuhair Abdul Ghafoor Al-Johar]

Dear Sirs, 

The below mentioned link refers to a simplification of a theory that 
I've presented to this list in a prior message (linked as post note). 

Structure Theory is a theory about Graphs and especially Trees. 
It extends General Extensional Atomic Mereology, so those graphs 
are defined in terms of Mereological totalities of nodes and edges 
which are stipulated to be atoms. Definition of paths, isomorphisms, 
trees and forests generally follow the customary known lines. 

Three structural rules are axiomatized which are: 

1. Extensionality: There exists a forest having a single isomorphic copy 
of each tree as a free (i.e. not a proper part of a tree in it) tree in it. 

2. Power: For every tree t there exists a tree T of all sub-trees of t. 

3. Functionality: For every formula phi defining an injective map from 
a forest A to a forest B, there is a graph composed of A and B as parts 
of, that has a single edge from each node x of A to node y of B that fulfill 
phi(x,y). 

Those rules are naive to this method which aims at constructing structures 
from the most simple (i.e., atoms) to the next complex in a stepwise manner, 
and with continuity versus discreetness interchange taken into account. 

These rules do interpret all axioms of ZFC. 

Details at: https://sites.google.com/site/zuhairaljohar/structure-theory
  

Best regards, 

Zuhair Al-Johar 
PS: earlier attempts at: http://www.cs.nyu.edu/pipermail/fom/2014-March/017902.html