Unitary representations of the groups of measurable and continuous functions with values in the circle

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second countable, zero-dimensional spaces with values in the circle. In the proofs of our classification results, certain structure theorems and factorization theorems for linear operators are used

"Acquired wit" and Hobbesian education

This thesis analyzes and evaluates the scheme for civil education discussed in Thomas Hobbes’ political works. Hobbes argues in The Elements of Law, De Cive, and Leviathan that the preservation of political order requires that all subjects learn the rationally grounded principles of political theory. Some contemporary scholarship on this aspect of Hobbes’ political philosophy has confined its understanding of “Hobbesian education” to this: the sovereign’s system of true civil doctrines and the means for their dissemination. I argue that for the system of Hobbesian civil doctrines to function as it is intended, a public must also receive instruction in formal argumentation, a skill Hobbes calls “acquired wit” (L viii.13). I will show that the subjects’ cultivation of their individual reasoning abilities is required so the subjects are able to (1) understand the philosophical foundations of the sovereign’s power, (2) sufficiently resist the allure of obfuscating eloquence and other falsehoods, and (3) conduct themselves in accordance with Hobbes’ natural laws. Civil peace in a Hobbesian system requires that the public be able to tell the difference between sound and unsound inferences. If Hobbes did intend for the sovereign to instruct the public in “acquired wit,” contemporary scholars who have offered sympathetic appraisals of Hobbesian education are further vindicated

Coherent extension of partial automorphisms, free amalgamation, and automorphism groups

We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fraisse classes. We deduce from these results that the isometry group of the rational Urysohn space, the automorphism group of the Fraisse limit of any Fraisse class that is the class of all $\mathcal{F}$-free structures (in the Herwig--Lascar sense), and the automorphism group of any free homogeneous structure over a finite relational language, all contain a dense locally finite subgroup. We also show that any free homogeneous structure admits ample generics.Comment: 27 page

Pollution Prevention: Factors Behind Toxic Release Reduction in the U.S. Paper Industry

Drs. Tiefenbacher and Solecki analyze the factors associated with, and influential in, the reduction of toxic releases in the U.S. paper industry