We show that while the length ω iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Př́ıkrý forcing, it is consistent that no iteration of length greater than ω (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a general...

Some 40 years ago, Dana Scott proved that every countable Scott set is the standard system of a model of PA. Two decades later, Knight and Nadel extended his result to Scott sets of size ω1. Here, I show that assuming the Proper Forcing Axiom (PFA), every proper Scott set is the standard system of a model of PA. I define that a Scott set X is proper if it is arithmetically closed and the quotie...

Posner and Robinson [4] proved that if S ⊆ ω is non-computable, then there exists a G ⊆ ω such that S ⊕ G ≥T G′. Shore and Slaman [7] extended this result to all n ∈ ω, by showing that if S T ∅(n−1) then there exists a G such that S ⊕ G ≥T G(n). Their argument employs KumabeSlaman forcing, and so the set they obtain, unlike that of the Posner-Robinson theorem, is not generic for Cohen forcing i...

We (i.e. I) present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is the ideal generated by a Suslin ccc forcing (e.g. Lesbeque– null or meager), and P is a Suslin forcing, and P is I–preserving (i.e. it doesn’t make any positive Borel–set small), then P preserves generics over candidates and therefore is strongly I–preserving (i.e. doesn’t make any positi...

Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multiple-input multiple-output (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering environment. Realistic channels corresponding to scattering clusters exhibit correlated fading and...

The class forcing theorem, which asserts that every class forcing notion P admits a forcing relation P, that is, a relation satisfying the forcing relation recursion—it follows that statements true in the corresponding forcing extensions are forced and forced statements are true—is equivalent over Gödel-Bernays set theory GBC to the principle of elementary transfinite recursion ETROrd for class...

Changes of the Asian summer monsoon in response to anthropogenic forcing are examined using observations and phase 5 of the Coupled Model Intercomparison Project (CMIP5) multimodel, multirealization ensemble. In the twentieth century, CMIP5 models indicate a predominantly drying Asian monsoon, while in the twenty-first century under the representative concentration pathway 8.5 (RCP8.5) scenario...

Previous studies on the response of the South Asian summer monsoon to the direct radiative forcing caused by anthropogenic absorbing aerosols have emphasized the role of premonsoonal aerosol forcing. This study examines the roles of aerosol forcing in both preand postonset periods using the Community Earth SystemModel, version 1.0.4, with the CommunityAtmosphereModel, version 4. Simulations wer...

In a systematic study, we compare the density statistics in high resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing....