A new way for the foundation of set theory
Date: Mon, 21 Dec 2015 08:00:01 -0800 (PST)
Message-ID: <b0765cc5-61d6-4508-9357-495328bbc6b4_at_googlegroups.com>
Elements of a set are names.
A set is a plurality of names which is named with one name.
The first three constructs of this set theory are as follows:
- Construct1: Frege's definition of concept.
- Construct2: Frege's assumption of extensions of concepts
- My theory of identification.
Definition:
Two sets A and B have the same cardinality if there exists an algorithm that
can show that every element of A is paired with exactly one element of B,
and every element of B is paired with exactly one element of A. There are no
unpaired elements.
Example:
We can form two columns. In the first column, we can store the names from
set A, and in the second column are stored the names from set B. The first
column we'll call "First name", the second column we'll call "Last name". If
at some point in these two columns exist gaps, then the two set do not have
the same cardinality.
Note that here we have an algorithm, rather than the 1-1 mapping. In fact,
some machine can "see" a gap in the columns, from this example.
This set theory is based on the objects, which are defined in my papers. In these papers are also introduced the atomic structure (atomic objects, atomic propositions, atomic predicates, atomic concepts, atomic facts and
atomic sets).My papers also define the following states of objects and relationships: current states, past states and future states.
Vladimir Odrljin Received on Mon Dec 21 2015 - 17:00:01 CET