Correction of the Big Bang theory and cyclic universe

In the present paper we establish, that the universe is eternal, that is it has no beginning and no end in the time. If we accept the original Big Bang theory, i.e. that the universe has arose from an extremely small, dense and hot fireball by an unique big bang and an inflation which continues until now, then we prove, using the axiomatic method, that (i) there exists an infinite number of big bangs in the past and in the future and (ii) the universe is cyclic. Furthermore we prove directly that the universe is cyclic without an using of a big bang of the universe. The statement (i) can be regarded as a correction of the original Big Bang theory.