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The thesis is devoted to the cardinal arithmetic. The first step is to formulate the Singular Cardinals Hypothesis (SCH) which simplifies the cardinal exponentiation of sin- gular cardinal numbers. We then define stationary sets and closed and unbounded subsets of an ordinal number. The main goal is to prove the Silver's theorem and the corollary which states, that if SCH holds for all singular cardinals with countable cofinality, then it holds everywhere. In the last chapter we define strongly compact cardinal numbers and prove some of their properties. Finally, we prove the Solovay's theorem, which states that SCH holds everywhere above a strongly compact cardinal. 1 |
