A. Miller    Math 873   Fall 98 
   Forcing in your face until it comes out your ear 

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Prerequisite: 771

Textbook: Set Theory, On the structure of the Real Line, Tomek
 Bartoszynski, Haim Judah, published by AK Peters (1995).

DESCRIPTION:  Measure and category on the real line and set theory.  This
includes consistency results using the method of forcing as well as
theorems provable in ZFC.  An example of the latter is a result of
Bartoszynski:
 The addivity of measure is less than or equal to the additivity of
category.
 (The additivity of measure is the least cardinality of a family of
Lebesgue measure zero sets whose union does not have measure zero.  The
additivity of category is defined similarly with first category replacing
measure zero.) 
 An example of the former is the independence of the Borel Conjecture (BC) 
from the axioms of ZFC due to Laver and Sierpinski. 
    (BC)  Every strong measure zero set of reals is countable. 
 (A set of reals X has strong measure zero iff for any sequence of
positive reals e(0),e(1),e(2),... the set X can be partitioned into sets
X(0),X(1),X(2),...  where each X(n) has diameter less than e(n).)