Finitely Generated Groups Are Universal

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same computability-theoretic properties as the given structure. Many classes such as graphs, groups, and fields are known to be universal. This paper is about the class of finitely generated groups. Because finitely generated structures are relatively simple, the class of finitely generated groups has no hope of being universal. We show that finitely generated groups are as universal as possible, given that they are finitely generated: for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties. The same is not true for finitely generated fields. We apply the results of this investigation to quasi Scott sentences

A summary of research relating to second and third grade reading

Thesis (Ed.M.)--Boston UniversityPURPOSE: To discover the reliability of the adjustment scale using two raters. This study was conducted to help determine whether the instrument used in this study gives a reliable measure of classroom adjustment. PROCEDURE: The teacher checklist of classroom adjustment devised at Boston University School of Education was the instrument used. The instrument was built to follow the activities of a normal classroom day [TRUNCATED