  We present a survey of some results of the pcf-theory and their applications
to cardinal arithmetic. We review basics notions (in section 1), briefly look
at history in section 2 (and some personal history in section 3). We present
main results on pcf in section 5 and describe applications to cardinal
arithmetic in section 6. The limitations on independence proofs are discussed
in section 7, and in section 8 we discuss the status of two axioms that arise
in the new setting. Applications to other areas are found in section 9.
