We investigate the consistency strength of the forcing axiom for Σ3 formulas, for various classes of forcings. We review that the consistency strength of Σ3-absoluteness for all set forcing or even just for ω1-preserving forcing is that of a reflecting cardinal. To get the same strength from the forcing axiom restricted to proper forcing, one can add the hypotheses that ω1 is inaccessible to re...

We study the projective posets and their properties as forcing notions. We also define Martin’s axiom restricted to projective sets, MA(proj), and show that this axiom is weaker than full Martin’s axiom by proving the consistency of ZFC + XH + MA(proj) with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists K < 2No such that...

Both the Continuum Hypothesis and Martin's Axiom allow induc-tive constructions to continue in circumstances where the inductive hypothesis might otherwise fail. The search for useful related axioms procedes naturally in two directions: towards "Super Martin's Axioms ," which extend MA to broader classes of orders; and towards "Anti-Martin's Axioms" (AMA's) which are strictly weaker than CH, bu...

The notion of realizability algebra, which was introduced in [17, 18], is a tool to study the proof-program correspondence and to build new models of set theory, which we call realizability models of ZF. It is a variant of the well known notion of combinatory algebra, with a new instruction cc, and a new type for the environments. The sets of forcing conditions, in common use in set theory, are...

Due to the large number of users and the time-varying characteristics of wireless channels, it is very tough to inform the transmitter of full channel information in real multi-user MIMO broadcast systems. On the other hand, the capacity of multi-user systems greatly depends on the knowledge of the channel at the transmitter while this is not always the case in single-user MIMO systems. In this...

The focus of this paper is on spatial precoding in correlated multi-antenna channels, where the number of independent data-streams is adapted to trade-off the data-rate with the transmitter complexity. Towards the goal of a low-complexity implementation, a structured precoder is proposed, where the precoder matrix evolves fairly slowly at a rate comparable with the statistical evolution of the ...

To reduce acoustic feedback in hearing aids, adaptive filters are commonly used to estimate the feedback contribution in the microphone(s). While theoretically allowing for perfect feedback cancellation, in practice the solution is typically biased due to the closed-loop acoustical system. For an earpiece with multiple integrated microphones and loudspeakers, we propose to use a fixed beamforme...

This correspondence examines Tomlinson–Harashima precoding (THP) on discrete-time channels having intersymbol interference and additive white Gaussian noise. An exact expression for the maximum achievable information rate of zero-forcing (ZF) THP is derived as a function of the channel impulse response, the input power constraint, and the additive white Gaussian noise variance. Information rate...

On Subcomplete Forcing by Kaethe Lynn Bruesselbach Minden Adviser: Professor Gunter Fuchs I survey an array of topics in set theory and their interaction with, or in the context of, a novel class of forcing notions: subcomplete forcing. Subcomplete forcing notions satisfy some desirable qualities; for example they don’t add any new reals to the model, and they admit an iteration theorem. While ...