Forbidden rectangles in compacta

We establish negative results about "rectangular" local bases in compacta. For example, there is no compactum where all points have local bases of cofinal type \omega x \omega_2. For another, the compactum \beta\omega has no nontrivially rectangular local bases, and the same is consistently true of \beta\omega \ \omega: no local base in \beta\omega has cofinal type \kappa x c if \kappa < m_{\sigma-n-linked} for some n in [1,\omega). Also, CH implies that every local base in \beta\omega \ \omega has the same cofinal type as one in \beta\omega. We also answer a question of Dobrinen and Todorcevic about cofinal types of ultrafilters: the Fubini square of a filter on \omega always has the same cofinal type as its Fubini cube. Moreover, the Fubini product of nonprincipal P-filters on \omega is commutative modulo cofinal equivalence.Comment: 15 page

Non-Absoluteness of Model Existence at ℵω\aleph_\omega

In [FHK13], the authors considered the question whether model-existence of $L_{\omega_1,\omega}$-sentences is absolute for transitive models of ZFC, in the sense that if $V \subseteq W$ are transitive models of ZFC with the same ordinals, $\varphi\in V$ and $V\models "\varphi \text{ is an } L_{\omega_1,\omega}\text{-sentence}"$, then $V \models "\varphi \text{ has a model of size } \aleph_\alpha"$ if and only if $W \models "\varphi \text{ has a model of size } \aleph_\alpha"$. From [FHK13] we know that the answer is positive for $\alpha=0,1$ and under the negation of CH, the answer is negative for all $\alpha>1$. Under GCH, and assuming the consistency of a supercompact cardinal, the answer remains negative for each $\alpha>1$, except the case when $\alpha=\omega$ which is an open question in [FHK13]. We answer the open question by providing a negative answer under GCH even for $\alpha=\omega$. Our examples are incomplete sentences. In fact, the same sentences can be used to prove a negative answer under GCH for all $\alpha>1$ assuming the consistency of a Mahlo cardinal. Thus, the large cardinal assumption is relaxed from a supercompact in [FHK13] to a Mahlo cardinal. Finally, we consider the absoluteness question for the $\aleph_\alpha$-amalgamation property of $L_{\omega_1,\omega}$-sentences (under substructure). We prove that assuming GCH, $\aleph_\alpha$-amalgamation is non-absolute for $1<\alpha<\omega$. This answers a question from [SS]. The cases $\alpha=1$ and $\alpha$ infinite remain open. As a corollary we get that it is non-absolute that the amalgamation spectrum of an $L_{\omega_1,\omega}$-sentence is empty

Crafting a Career Using CPS and FourSight

ABSTRACT OF PROJECT Crafting a Career Using CPS and FourSight The purpose of my project is to develop a case study of how I will use Creative Problem Solving (CPS) and an attention to my Foursight preferences to grow my existing craft business into a viable career, rather than having it as just a hobby. By utilizing the CPS Thinking Skills Model and having a greater awareness of my Foursight preferences, I was able to move from a dream to a reality and come out the other end of this project with a fully functioning, profitable business rooted firmly in creativity. This project was two fold in nature: I spent a great deal of time using CPS and its various tools as well as enhancing the Foursight preferences that are not mine naturally. I then reported in a case study fashion how this introspection has effected my craft business

Noetherian types of homogeneous compacta and dyadic compacta

AbstractThe Noetherian type of a space is the least κ such that it has a base that is κ-like with respect to reverse inclusion. Just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactum has Noetherian type ω. Assuming GCH, every point in a homogeneous compactum X has a local base that is c(X)-like with respect to containment. If every point in a compactum has a well-quasiordered local base, then some point has a countable local π-base

From Technology Revolution to Digital Revolution: An Interview with F. Warren McFarlan from the Harvard Business School

In this paper, I recount an interview I had with F. Warren McFarlan, DBA, a senior scholar whose passion to keep working in information systems (IS) overrode his two attempts at retirement in 2004 and again in 2009. His 50 years of knowledge builds on experience from companies in the United States and Asia, both large corporations and start-ups, and for-profit and nonprofit companies. Additionally, he has helped develop the minds of generations of business leaders through his work at the Harvard Business School (HBS). Through the years, he has developed and taught IS case studies on companies that range from Chase Manhattan Bank to Alibaba. Given his enduring work in technology, these interviews provide interesting insight into coursework development at HBS, the frequent redefinition of the digital native, the language of business versus that of IT, a management stance on IT, the management of IT projects, work on for-profit and nonprofit boards, and a view on China and IS