From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.

We prove various theorems about the preservation and destruction of the tree property at ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we (...) prove from a supercompact cardinal that the tree property at ω2 can be indestructible under ω2-directed closed forcing. (shrink)

In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\nu $ such that the singular cardinal hypothesis fails at $\nu $ and every collection of fewer than $\operatorname {\mathrm {cf}}(\nu )$ stationary subsets of $\nu ^{+}$ reflects simultaneously. For $\operatorname {\mathrm {cf}}(\nu )> \omega $, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for (...) $\operatorname {\mathrm {cf}}(\nu ) = \omega $ to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon. (shrink)

We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD. We also answer a related question of Cummings, Friedman and Golshani by producing a model in which every regular uncountable cardinal [Formula: see text] in [Formula: see text] is [Formula: see text]-supercompact in HOD.

We construct a model in which the singular cardinal hypothesis fails at ℵωℵω. We use characterizations of genericity to show the existence of a projection between different Prikry type forcings.

Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular $k>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.

We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.

We present an alternative proof that from large cardinals, we can force the tree property at $\kappa ^+$ and $\kappa ^{++}$ simultaneously for a singular strong limit cardinal $\kappa $. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for $\kappa =\aleph _{\omega ^2}$.

This article investigates the role of Big Data in situations of psychological stress such as during the recent pandemic caused by the COVID-19 health crisis. Quarantine measures, which are necessary to mitigate pandemic risk, are causing severe stress symptoms to the human body including mental health. We highlight the most common impact factors and the uncertainty connected with COVID-19, quarantine measures, and the role of Big Data, namely, how Big Data can help alleviate or mitigate these effects by comparing the (...) status quo of current technology capabilities with the potential effects of an increase of digitalization on mental health. We find that, while Big Data helps in the pre-assessment of potentially endangered persons, it also proves to be an efficient tool in alleviating the negative psychological effects of quarantine. We find evidence of the positive effects of Big Data on human health conditions by assessing the effect of internet use on mental health in 173 countries. We found positive effects in 110 countries with 90 significant results. However, increased use of digital media and exclusive exposure to digital connectivity causes negative long-term effects such as a decline in social empathy, which creates a form of psychological isolation, causing symptoms of acute stress disorder. (shrink)

We show that it is consistent, relative to ω many supercompact cardinals, that the super tree property holds at for all but there are weak square and a very good scale at.

Some argue that individuals and organizations doing business in countries where corruption is prevalent should not be expected to adhere to strict standards of ethical practice. The basis for such arguments is faulty. Ethics, unlike etiquette, has a universal basis; it is fundamentally the same all over the world. Even in a practical sense, there are long range advantages to be gained by ethical behavior in these situations. Engineering employees of companies operating in areas where corruption is common are sometimes (...) forced to make very difficult decisions. The focus in this paper is on the ethical aspects of the problem. Laws applying to companies doing business abroad, for example the US Corrupt Practices Act, are not discussed. (shrink)

Nine examples are presented illustrating the kinds of problems encountered in actual practice by conscientious engineers. These cases are drawn fom the records of the IEEE Ethics Committee, and from the experience of the ethics help-line initiated recently by the Online Ethics Center for Engineering and Science. They range from situations in which companies try to cheat one another to those in which human health and safety are jeopardized. In one case, an engineer learned that even a quiet resignation can (...) prove very costly in a personal sense. Some ways in which professional societies might make ethical practice of engineering somewhat easier are mentioned. (shrink)