Softcover ISBN:  9780821850916 
Product Code:  CONM/84 
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Electronic ISBN:  9780821876725 
Product Code:  CONM/84.E 
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Book DetailsContemporary MathematicsVolume: 84; 1989; 116 ppMSC: Primary 03; Secondary 54;
This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the “Sspace problem,” the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively settheoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.

Table of Contents

Chapters

Introduction

0. The role of countability in (S) and (L)

1. Oscillating real numbers

2. The conjecture (S) for compact spaces

3. Some problems closely related to (S) and (L)

4. Diagonalizations of length continuum

5. (S) and (L) and the Souslin Hypothesis

6. (S) and (L) and Luzin spaces

7. Forcing axioms for $ccc$ partitions

8. Proper forcing axiom and partitions.

9. (S) and (L) are different

References

Index of symbols

Index of terms


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This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the “Sspace problem,” the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively settheoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.

Chapters

Introduction

0. The role of countability in (S) and (L)

1. Oscillating real numbers

2. The conjecture (S) for compact spaces

3. Some problems closely related to (S) and (L)

4. Diagonalizations of length continuum

5. (S) and (L) and the Souslin Hypothesis

6. (S) and (L) and Luzin spaces

7. Forcing axioms for $ccc$ partitions

8. Proper forcing axiom and partitions.

9. (S) and (L) are different

References

Index of symbols

Index of terms