# [FOM] A simplification of Structure Theory.

Zuhair Abdul Ghafoor Al-Johar zaljohar at yahoo.com
Sun Dec 20 16:37:23 EST 2015

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.