Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which (...) is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops). (shrink)

A varietyV satisfies a strong Malcev condition ∃f1,…, ∃fnθ where θ is a conjunction of equations in the function variablesf1, …,fnand the individual variablesx1, …,xm, if there are polynomial symbolsp1, …,pnin the language ofVsuch that ∀x1, …,xmθ is a law ofV. Thus a strong Malcev condition involves restricted second order quantification of a strange sort. The quantification is restricted to functions which are “polynomially definable”. This notion was introduced by Malcev [6] who used it to describe those varieties all of (...) whose members have permutable congruence relations. The general formal definition of Malcev conditions is due to Grätzer [1]. Since then and especially since Jónsson's [3] characterization of varieties with distributive congruences there has been extensive study of strong Malcev conditions and the related concepts: Malcev conditions and weak Malcev conditions.In [9], Taylor gives necessary and sufficient semantic conditions for a class of varieties to be defined by a Malcev condition. A key to the proof is the translation of the restricted second order concepts into first order concepts in a certain many sorted language. In this paper we show that, given this translation, Taylor's theorem is an easy consequence of a result of Tarski [8] and the standard preservation theorems of first order logic. (shrink)

The immune system can generate an almost infinite number of different antibody specificities, the sum of which is the antibody repertoire. This article considers aspects of the mechanism and control of immunoglobulin variable (V) region gene assembly with a focus on how these factors may affect generation of the antibody repertoire in normal and disease states. New model systems to study the mechanism and control of V gene assembly are described, in particular the introduction of V gene recombination substrates into (...) Abelson murine leukemia virus‐transformed pre‐B cells. Finally, a model is presented which suggests that control of V gene assembly is mediated by regulating accessibility of substrate gene segments to recombinational machinery. (shrink)

(1999). The lessons and messages of the holocaust as conveyed through Yom Hashoah (holocaust day) commemorations in selected Australian Jewish communities, 1945–1996. The European Legacy: Vol. 4, Postmodern Fascism, pp. 54-71.

Few subjects have provoked more speculation or scholarly inquiry than the relationship between creativity and madness—or, in the case of Jason Thompson, the link between memoir writing and depression. Plato theorized that the poet’s madness is divinely inspired, and two thousand years later Sigmund Freud (1928/1961) admitted that “Before the problem of the creative artist analysis must, alas lay down its arms” (p. 177)—a cautionary injunction he then disregards. Should authors heed Thompson’s prudent advice not to write about present traumas, (...) or should they accept D. H. Lawrence’s (1981) statement that “One sheds one’s sicknesses in books, repeats and presents again one’s emotions, to be master of them” (p. .. (shrink)

Sustainable Learning: Inclusive Practices for 21st Century Classrooms provides readers with the knowledge and skills to be confident and effective inclusive teachers. The authors show that these skills are essential to quality teaching – teaching that is evidence-based, purposeful, relevant and responsive to students' needs. The book employs three overarching frameworks to examine inclusive practices in education: equity, values and sustainability. Chapter features include: • 'Think and do' exercises • Examples, case studies and vignettes • Tables, figures and diagrams to (...) help readers visualise core ideas, theories and themes. It encourages teachers to see all students as developing learners and to consider the complexities and diversity of learning in the 21st century. In doing so, it canvasses topics such as a sustainable approach to inclusion, learning processes, teaching processes, differentiation, assessment to support teaching and learning, and life-long learning. (shrink)