24,749 research outputs found
Realizability algebras II : new models of ZF + DC
Using the proof-program (Curry-Howard) correspondence, we give a new method
to obtain models of ZF and relative consistency results in set theory. We show
the relative consistency of ZF + DC + there exists a sequence of subsets of R
the cardinals of which are strictly decreasing + other similar properties of R.
These results seem not to have been previously obtained by forcing.Comment: 28
Dependent choice, properness, and generic absoluteness
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to -preserving symmetric submodels of forcing extensions. Hence, not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the presence of large cardinals. We also investigate some basic consequences of the Proper Forcing Axiom in, and formulate a natural question about the generic absoluteness of the Proper Forcing Axiom in and. Our results confirm as a natural foundation for a significant portion of classical mathematics and provide support to the idea of this theory being also a natural foundation for a large part of set theory
Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
Assuming the existence of certain large cardinal numbers, we prove that for
every projective filter over the set of natural numbers,
-bases in Banach spaces have continuous coordinate functionals. In
particular, this applies to the filter of statistical convergence, thereby we
solve a problem by V. Kadets (at least under the presence of certain large
cardinals). In this setting, we recover also a result of Kochanek who proved
continuity of coordinate functionals for countably generated filters (Studia
Math., 2012).Comment: 10 p
The bias field of dark matter haloes
This paper presents a stochastic approach to the clustering evolution of dark
matter haloes in the Universe. Haloes, identified by a Press-Schechter-type
algorithm in Lagrangian space, are described in terms of `counting fields',
acting as non-linear operators on the underlying Gaussian density fluctuations.
By ensemble averaging these counting fields, the standard Press-Schechter mass
function as well as analytic expressions for the halo correlation function and
corresponding bias factors of linear theory are obtained, thereby extending the
recent results by Mo and White. The non-linear evolution of our halo population
is then followed by solving the continuity equation, under the sole hypothesis
that haloes move by the action of gravity. This leads to an exact and general
formula for the bias field of dark matter haloes, defined as the local ratio
between their number density contrast and the mass density fluctuation. Besides
being a function of position and `observation' redshift, this random field
depends upon the mass and formation epoch of the objects and is both non-linear
and non-local. The latter features are expected to leave a detectable imprint
on the spatial clustering of galaxies, as described, for instance, by
statistics like bispectrum and skewness. Our algorithm may have several
interesting applications, among which the possibility of generating mock halo
catalogues from low-resolution N-body simulations.Comment: 23 pages, LaTeX (included psfig.tex), 4 figures. Few comments and
references have been added, and minor typos and errors corrected. This
version matches the refereed one, in press in MNRA
A simple test for normality for time series
This paper considers testing for normality for correlated data. The proposed test
procedure employs the skewness-kurtosis test statistic, but studentized by standard
error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities
that do not incorporate any downweighting, and, hence, no smoothing parameter
is needed. Therefore, the main feature of our proposed test is its simplicity, because
it does not require the selection of any user-chosen parameter such as a smoothing
number or the order of an approximating model.Publicad
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