Summary:
The main topic of this Master Thesis is Ramsey theory. Firstly we prove three
basic theorems of the classical Ramsey theory, the Ramsey theorem, the
Nash-Williams theorem and Ellentuck's theorem.
Defining the thin Schreier families of finite subsets of natural numbers,
defined by Farmaki, and the strong Cantor-Bendixson index, we prove an extended
Ramsey theory, developed by Farmaki,
including a Ramsey theorem for every countable ordinal, a stronger form of
Nash-Williams partition theorem and a new proof of Elentuck's theorem.
Keywords:
Ramsey, Nash-Williams, Ellentuck, Schreier
