Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Kanamori in the introduction of his famous book "The Higher Infinite" says that his book is the first volume of a complete book and the second volume is about large cardinals and forcing. I saw several papers which refer to its content.

Question (1): When the volume II of "The Higher Infinite" will be published?

Question (2): Does anybody have a preprint of this volume?

share|improve this question
    
If you're just looking for a good source of information on more topics you could check out the Handbook of Set Theory, which is edited by Kanamori and Foreman and might be thought of as some form of spiritual successor. handbook.assafrinot.com –  Tim Mercure Sep 29 '13 at 14:53
3  
As far as I know, the volume does not exist. It is not clear there is a need for it anymore, thanks to the Handbook, but you'd have to ask Kanamori directly whether he plans to continue work on it (the first volume was also years in the making). There were some chapters circulated informally, I know of two (which may be all there was). One on Chang conjectures, subtle cardinals, diamond, and related combinatorial principles. The other was on $K$, at the level of measurable cardinals. Both would need updating by now. –  Andres Caicedo Sep 29 '13 at 16:39
1  
(The two chapters I have seen are VI and VIII as in Mohammad's list). –  Andres Caicedo Sep 29 '13 at 16:41

1 Answer 1

up vote 12 down vote accepted

There are some papers in which "The higher infinite II" is given as references:

1) Forcing Axioms and the Continuum Problem -Sakae Fuchino

2) The mathematical development of set theory from Cantor to Cohen-Kanamori,

3) Distributivity properties on $P_\omega(\lambda)$-Matet.

But I have no idea about if the book is going to be published or not.

Even the following content is presented for the book (note that the book is a continuation of volume I, so it starts with chapter VI)!!!!

Chapter VI. Higher Combinatorics

Kurepa's Hypothesis and Chang's Conjecture Combinatorial Principles Subtle Properties The Tree Property

Chapter VII. Forcing with Strong Hypotheses I

Master Conditions (Silver's upward Easton forcing, Kunen's saturated ideal)

Ultrafilters (structure theory, combinatorics)

Singular Cardinals Problem (intro, Solovay's result, ultrafilters, Silver's result)

Strong vs. Supercompactness

Singular Cardinals Problem Forcing (Magidor's earlier results)

Precipitous Ideals (combinatorics, equiconsistency with measurable)

Chapter VIII. Covering and the Core Model

The Covering Theorem for $L$

The Core Model

Models and Mice

The Covering Theorems for $K$ and for $L[U]$

Applications of $K$

Chapter IX. Higher Combinatorics II

Reflecting stationary sets, Shelah's LM result, etc.

Chapter X. Forcing with Strong Hypotheses II

Radin forcing, Proper forcing, forcing axioms

Chapter XI. Consistency Results about AD

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.