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Fundamentals of foundation engineering
\"This book aims to introduce the principal and design of various foundations, covering shallow foundations, mat foundations, earth retaining structures, excavations, pile foundations, and slope stability. Since the analysis and design of a foundation are based on the soil properties under short-term (undrained) or long-term (drained) conditions, the assessment of soil properties from the geotechnical site investigation and the concept of drained or undrained soil properties are discussed in the first two chapters. Foundation elements transfer various load combinations from the superstructure to the underlying soils or rocks. The load transfer mechanisms, vertical stress or earth pressure distributions, and failure modes of each foundation type are clearly explained in this book. After understanding the soil responses subjected to the loadings from the foundation, the design methods, required factors of safety, and improvement measures for each foundation type are elaborated. This book presents both theoretical explication and practical applications for readers to easily comprehend the theoretical background, design methods, and practical applications and considerations. Each chapter provides relevant exercise examples and a problem set for self-practice. The analysis methods introduced in the book can be applied in actual analysis and design as they contain the most up-to-date knowledge of foundation design. This book is suitable for teachers and students to use in foundation engineering courses, and engineers who are engaged in foundation design to create a technically sound, construction-feasible, and economical design of the foundation system\"-- Provided by publisher.
Book
textsf {AD}^{+}$ implies $ \\omega _{1}$ is a club $ \\Theta $ -Berkeley cardinal
Following [1], given cardinals
$\\kappa <\\lambda $
, we say
$\\kappa $
is a club
$\\lambda $
-Berkeley cardinal if for every transitive set N of size
$<\\lambda $
such that
$\\kappa \\subseteq N$
, there is a club
$C\\subseteq \\kappa $
with the property that for every
$\\eta \\in C$
, there is an elementary embedding
$j: N\\rightarrow N$
with
$\\mathrm {crit }(j)=\\eta $
. We say
$\\kappa $
is
$\\nu $
-club
$\\lambda $
-Berkeley if
$C\\subseteq \\kappa $
as above is a
$\\nu $
-club. We say
$\\kappa $
is
$\\lambda $
-Berkeley if C is unbounded in
$\\kappa $
. We show that under
$\\textsf {AD}^{+}$
, (1) every regular Suslin cardinal is
$\\omega $
-club
$\\Theta $
-Berkeley (see Theorem 7.1), (2)
$\\omega _1$
is club
$\\Theta $
-Berkeley (see Theorem 3.1 and Theorem 7.1), and (3) the ’s are
$\\Theta $
-Berkeley – in particular,
$\\omega _2$
is
$\\Theta $
-Berkeley (see Remark 7.5). Along the way, we represent regular Suslin cardinals in direct limits as cutpoint cardinals (see Theorem 5.1). This topic has been studied in [31] and [4], albeit from a different point of view. We also show that, assuming
$V=L({\\mathbb {R}})+{\\textsf {AD}}$
,
$\\omega _1$
is not
$\\Theta ^+$
-Berkeley, so the result stated in the title is optimal (see Theorem 9.14 and Theorem 9.19).
Journal Article
mathbf {\\Sigma }_1$ -definability at higher cardinals: Thin sets, almost disjoint families and long well-orders
Given an uncountable cardinal
$\\kappa $
, we consider the question of whether subsets of the power set of
$\\kappa $
that are usually constructed with the help of the axiom of choice are definable by
$\\Sigma _1$
-formulas that only use the cardinal
$\\kappa $
and sets of hereditary cardinality less than
$\\kappa $
as parameters. For limits of measurable cardinals, we prove a perfect set theorem for sets definable in this way and use it to generalize two classical nondefinability results to higher cardinals. First, we show that a classical result of Mathias on the complexity of maximal almost disjoint families of sets of natural numbers can be generalized to measurable limits of measurables. Second, we prove that for a limit of countably many measurable cardinals, the existence of a simply definable well-ordering of subsets of
$\\kappa $
of length at least
$\\kappa ^+$
implies the existence of a projective well-ordering of the reals. In addition, we determine the exact consistency strength of the nonexistence of
$\\Sigma _1$
-definitions of certain objects at singular strong limit cardinals. Finally, we show that both large cardinal assumptions and forcing axioms cause analogs of these statements to hold at the first uncountable cardinal
$\\omega _1$
.
Journal Article
Decidability of the class of all the rings $\\mathbb {Z}/m\\mathbb {Z}$ : A problem of Ax
We prove that the class of all the rings
$\\mathbb {Z}/m\\mathbb {Z}$
for all
$m>1$
is decidable. This gives a positive solution to a problem of Ax asked in his celebrated 1968 paper on the elementary theory of finite fields [1, Problem 5, p. 270]. In our proof, we reduce the problem to the decidability of the ring of adeles
$\\mathbb {A}_{\\mathbb {Q}}$
of
$\\mathbb {Q}$
.
Journal Article
No such thing as a free gift : the Gates Foundation and the price of philanthropy
Philanthro-capitalism: How charity became big business. The charitable sector is one of the fastest-growing industries in the global economy. Nearly half of the more than 85,000 private foundations in the United States have come into being since the year 2000. Just under 5,000 more were established in 2011 alone. This deluge of philanthropy has helped create a world where billionaires wield more power over education policy, global agriculture, and global health than ever before. Charities link the farmers in Africa to the boardrooms of corporate foundations and the corridors of the World Economic Forum at Davos. Far from being selfless, plutocratic philanthropy may be the ultimate profit-making tool. In this work, author and academic Linsey McGoey puts this new golden age of philanthropy under the microscope--paying particular attention to the Bill and Melinda Gates Foundation. As large charitable organizations replace governments as the providers of social welfare, their largesse becomes suspect. The businesses fronting the money often create the very economic instability and inequality the foundations are purported to solve. We are entering an age when the ideals of social justice are dependent on the strained rectitude and questionable generosity of the mega-rich.
Book
Souslin quasi-orders and bi-embeddability of uncountable structures
We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond
to the case
eBook