Set Theory of The Real Line
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High Quality Content by WIKIPEDIA articles! Set theory of the real line is an area of mathematics concerned with the application of set theory to aspects of the real numbers. If one restricts to specific forcings, some invariants will become big while others remain small. Analysing these effects is the major work of the area, seeking to determine which inequalities between invariants are provable and which are inconsistent with ZFC. This analysis is substantially complete. The inequalities among the ideals of measure (null sets) and category (meagre sets) are captured in Cichon's diagram.…mehr

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High Quality Content by WIKIPEDIA articles! Set theory of the real line is an area of mathematics concerned with the application of set theory to aspects of the real numbers. If one restricts to specific forcings, some invariants will become big while others remain small. Analysing these effects is the major work of the area, seeking to determine which inequalities between invariants are provable and which are inconsistent with ZFC. This analysis is substantially complete. The inequalities among the ideals of measure (null sets) and category (meagre sets) are captured in Cichon's diagram. Seventeen models (forcing constructions) were produced during the 1980s, starting with work of Arnold Miller, to demonstrate that no other inequalities are provable. These are analysed in detail in the book by Tomek Bartoszynski and Haim Judah, two of the eminent workers in the field.