9,394 research outputs found
A hierarchy of Ramsey-like cardinals
We introduce a hierarchy of large cardinals between weakly compact and
measurable cardinals, that is closely related to the Ramsey-like cardinals
introduced by Victoria Gitman, and is based on certain infinite filter games,
however also has a range of equivalent characterizations in terms of elementary
embeddings. The aim of this paper is to locate the Ramsey-like cardinals
studied by Gitman, and other well-known large cardinal notions, in this
hierarchy
Stable Recovery from the Magnitude of Symmetrized Fourier Measurements
In this note we show that stable recovery of complex-valued signals
up to global sign can be achieved from the magnitudes of
Fourier measurements when a certain "symmetrization and zero-padding" is
performed before measurement ( is possible in certain cases). For real
signals, symmetrization itself is linear and therefore our result is in this
case a statement on uniform phase retrieval. Since complex conjugation is
involved, such measurement procedure is not complex-linear but recovery is
still possible from magnitudes of linear measurements on, for example,
.Comment: 4 pages, will be submitted to ICASSP1
Class forcing, the forcing theorem and Boolean completions
The forcing theorem is the most fundamental result about set forcing, stating
that the forcing relation for any set forcing is definable and that the truth
lemma holds, that is everything that holds in a generic extension is forced by
a condition in the relevant generic filter. We show that both the definability
(and, in fact, even the amenability) of the forcing relation and the truth
lemma can fail for class forcing. In addition to these negative results, we
show that the forcing theorem is equivalent to the existence of a (certain kind
of) Boolean completion, and we introduce a weak combinatorial property
(approachability by projections) that implies the forcing theorem to hold.
Finally, we show that unlike for set forcing, Boolean completions need not be
unique for class forcing
Applying Science Models for Search
The paper proposes three different kinds of science models as value-added
services that are integrated in the retrieval process to enhance retrieval
quality. The paper discusses the approaches Search Term Recommendation,
Bradfordizing and Author Centrality on a general level and addresses
implementation issues of the models within a real-life retrieval environment.Comment: 14 pages, 3 figures, ISI 201
Forcing lightface definable well-orders without the CGH
For any given uncountable cardinal with , we present a forcing that is -directed closed, has the -c.c. and introduces a lightface definable well-order of . We use this to define a global iteration that does this for all such simultaneously and is capable of preserving the existence of many large cardinals in the universe
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