Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

A simple proof of Tychonoff’s theorem (the compactness of the product of compact spaces) as a direct application of Zorn’s lemma is given. In contrast to the classical Cartan-Bourbaki proof which uses Zorn’s lemma twice, our proof uses it only once.

Using Zorn’s lemma one can show that order closures always exist [Cl, Sect. 43. This is the first systematic treatment of such fields, though they have also been used in [C2]. A major problem in dealing with order closed fields is that it is not clear whether or not they have algebraic extensions to which all orderings extend (necessarily nonuniquely). This leads us to make the following defini...

function on A is thus a choice of an element of the variable set A at each stage; in other words, a choice function on A is just a variable (or global) element of A . The axiom of choice (AC) asserts that if each member of a family A is nonempty, then there is a choice function on A . Metaphorically, then, the axiom of choice asserts that any family of sets with an element at each stage has a v...

Various authors use the Bunge-Wand-Weber-model (BWW-model) [We97] for evaluating grammars [Sh03]. In this presentation, we apply the BWW-Model to ontological evaluate Scheer’s reference model for production planning and control systems (PPC) [Sc94]. This study follows the approach of [FL03a] in – at first – identifying ontological deficiencies of the grammar which is used to represent a referen...

by Robert B. Avery, Patricia E. Beeson, and Mark S. Sniderman Robert B. Avery is an associate professor in the Department of Consumer Economics and Housing, Cornell University, and Patricia E. Beeson is an associate professor of economics at the University of Pittsburgh; both are visiting scholars at the Federal Reserve Bank of Cleveland. MarkS. Sniderman is senior vice president and director o...

This paper describes the weight-length relationships (WLRs) and Fulton's condition factors (K) of skipjack tuna (Katsuwonus pelamis) in purse seine fisheries from three cruises in the western and central Pacific Ocean (WCPO): August-September 2009 (AS09), November-December 2012 (ND12), and June-July 2013 (JJ13). The fork length and weight of a total of 1678 specimens were measured. The results ...

In einer Reihe von Untersuchungen wird die philosophische Disziplin der Ontologie als Grundlage für die Informationsmodellierung verwendet. Aufbauend auf der Bunge-Ontologie wird in diesem Beitrag eine Vorgehensweise zur ontologischen Evaluierung von Referenzmodellen präsentiert und anhand des YCIM-Modells von Scheer exemplarisch angewendet.

A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the pre...