January 22, 2017 Sunday
Bedtime Story
ZFC: Axiomatic Set Theory and the Foundation of Mathematics
It is interesting to know why the name of Skolem was left out.
This was chiefly because the very influential and charismatic and
perhaps the most famous mathematician John von Neumann chose the phrase
“Zermelo-Fraenkel set theory” in print in 1928.
It perhaps stayed that way since then erasing out Skolem forever.
This new axiomatic system presented by Zermelo and Fraenkel goes
by the name of Zermelo-Fraenkel set theory or simply as ZF axiomatization.
The ZF axiomatization excludes that all powerful axiom of choice
that I took great pains to explain to you.
When Zermelo-Fraenkel does include the axiom of choice, then it
goes by the abbreviation of ZFC.
One of the outcomes of the ZFC is the establishment of von
Neumann’s universe of cumulative hierarchy that is denoted by V.
It is sometimes also known as von Neumann’s hierarchy of sets.
It is an example of a hereditary set which essentially means that
all elements of the set are themselves sets; and so are all the elements of the
elements and so it goes on.
This von Neumann’s universe of sets was actually first published
by Ernst Zermelo in 1930 though in 1928 von Neumann had published a paper on a
general transfinite recursive definition of sets.
Similarly, the notion V comes not from von Neumann’s name but from
the word “Verum” that was used by Giuseppe Peano in 1889 for the universe of
sets.
The set V is the set of all sets that are divided into transfinite
hierarchy that can be defined inductively.
We shall take up this von Neumann’s universe tomorrow in more
earnest.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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