Geared toward readers already acquainted with special relativity, this book transcends the view of theory as a working tool to answer natural questions: What is ...

. From a proper class of supercompact cardinals, we force and obtain a model in which the proper classes of strongly compact and strong cardinals precisely coincide. In this model, it is the case that no strongly compact cardinal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\kappa$\end{document} is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $2^\kappa = \kappa^+$\end{document} supercompact.

Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals κ 1 ,..., κ n are so that κ i for i = 1,..., n is both the i th measurable cardinal and κ + i supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.

Originally published 1968, the book examines the ways in which the definitions of education held by different groups with power have changed since 1800 and traces which social institutions exercised the preponderant influence on the growth of the English educational system during the seminal period in which the state system was founded and grew to its present position. Especial attention is given to the influence of the ideologies of the various social classes, to the growing demands of the economy on (...) the educational system and to changes in the structure of the family. (shrink)

We prove a consistency result about square principles and stationary reflection which generalises the result of Ben-David and Magidor [4].