Preface to Part I
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چکیده
Many interesting mathematical properties, especially concerning real analysis, are known to be true in the iterated perfect set (Sacks) model, while they are false under the continuum hypothesis. However, the proofs that these facts are indeed true in this model are usually very technical and involve heavy forcing machinery. In this manuscript we extract a combinatorial principle, an axiom similar to the Martin axiom, that is true in the model and show that this axiom implies the above mentioned properties in a simple “mathematical” way. The proofs are essentially simpler than the original arguments. To follow all but the last chapter of this manuscript only a moderate knowledge of set theory is required. No forcing knowledge is necessary.
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