We show that the Abraham–Rubin–Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with [Formula: see text]. This answers one of the main open questions from [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206]. As in [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for (...) continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206], we need to construct names for the so-called preassignments of colors in order to add the necessary homogeneous sets. However, the known constructions of preassignments (ours in particular) only work assuming the [Formula: see text]. In order to address this difficulty, we show how to construct such names with very strong symmetry conditions. This symmetry allows us to combine them in many different ways, using a new type of poset called a partition product. Partition products may be thought of as a restricted memory iteration with stringent isomorphism and coherent-overlap conditions on the memories. We finally construct, in [Formula: see text], the partition product which gives us a model of [Formula: see text] in which [Formula: see text]. (shrink)

For any Boolean Algebra A, let cmm be the smallest size of an infinite partition of unity in A. The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which cmm exceeds any preassigned number, a rigid interval algebra with that property, and the construction of an (...) interval algebra in which every well-ordered chain has size less than cmm. (shrink)

Analyses of errors from a sequential auditory recall experiment indicated that perceptual factors influence the shape of the serial position curve of recall errors. The signal to noise ratio and presentation rate of the stimuli, as well as presentation rate during a prior training session, affected item and order errors. For experiments in which Ss simply monitored the auditory sequences for a preassigned critical item, and in which items were recalled in addition to monitoring, analyses of montoring RTs provided evidence (...) that the requirement to recall induces perceptual difficulties. (shrink)

The Bell-Wigner locality argument is shown to be a special case of the nonexistence of certain state assembles with preassigned densities when there are restrictions on the allowable states.

This paper studies the adaptive event-triggered finite-time tracking of output-constrained high-order nonlinear systems with time-varying powers. Due to the presence of multiple unknown powers and the consideration of event-triggered control, all the existing control methods of output-constrained nonlinear systems are inapplicable. By introducing nonlinear mappings, finite-time performance functions, and low-power and high-power terms into adding a power integrator technique and the relative threshold strategy, an adaptive state-feedback controller is designed to eliminate the effects caused by the output constraint and time-varying (...) powers. It is proved that all the closed-loop signals are bounded, the asymmetric time-varying output constraint is not violated, and the tracking error converges to a prescribed arbitrarily small region around zero in a preassigned finite time. Furthermore, the Zeno phenomenon can be avoided. Two simulation examples demonstrate the effectiveness of this control scheme. (shrink)

In the past, hypothesis testing in medicine has employed the paradigm of the repeatable experiment. In statistical hypothesis testing, an unbiased sample is drawn from a larger source population, and a calculated statistic is compared to a preassigned critical region, on the assumption that the comparison could be repeated an indefinite number of times. However, repeated experiments often cannot be performed on human beings, due to ethical or economic constraints. We describe a new paradigm for hypothesis testing which uses only (...) rearrangements of data present within the observed data set. The token swap test, based on this new paradigm, is applied to three data sets from cardiovascular pathology, and computational experiments suggest that the token swap test satisfies the Neyman Pearson condition. (shrink)