The material conditions of non-domination: Property, independence, and the means of production

While it is a point of agreement in contemporary republican political theory that property ownership is closely connected to freedom as non-domination, surprisingly little work has been done to elucidate the nature of this connection or the constraints on property regimes that might be required as a result. In this paper, I provide a systematic model of the boundaries within which republican property systems must sit and explore some of the wider implications that thinking of property in these terms may have for republicans. The boundaries I focus on relate to the distribution of property and the application of types of property claims over particular kinds of goods. I develop this model from those elements of non-domination most directly related to the operation of a property regime: (a) economic independence, (b) limiting material inequalities, and (c) the promotion of common goods. The limits that emerge from this analysis support intuitive judgments that animate much republican discussion of property distribution. My account diverges from much orthodox republican theory, though, in challenging the primacy of private property rights in the realization of economic independence. The value of property on republican terms can be realized without private ownership of the means of production.

On the Lattice Properties of Almost L-Weakly and Almost M-Weakly Compact Operators

We establish the domination property and some lattice approximation properties for almost L-weakly and almost M-weakly compact operators. Then, we consider the linear span of positive almost L-weakly (resp., almost M-weakly) compact operators and give results about when they form a Banach lattice and have an order continuous norm.

Lower Convergence of Minimal Sets in Star-Shaped Vector Optimization Problems

LetAnbe a sequence of nonempty star-shaped sets. By using generalized domination property, we study the lower convergence of minimal setsMin An. The distinguishing feature of our results lies in disuse of convexity assumptions (only using star-shapedness).

Canonical functions, non-regular ultrafilters and Ulam's problem on ω1

Our main results are:Theorem 1. Con(ZFC + “every function f: ω1 → ω1 is dominated by a canonical function”) implies Con(ZFC + “there exists an inaccessible limit of measurable cardinals”). [In fact equiconsistency holds.]Theorem 3. Con(ZFC + “there exists a non-regular uniform ultrafilter on ω1”) implies Con(ZFC + “there exists an inaccessible stationary limit of measurable cardinals”).Theorem 5. Con (ZFC + “there exists an ω1-sequence of ω1-complete uniform filters on ω1 s.t. every A ⊆ ω1 is measurable w.r.t. a filter in (Ulam property)”) implies Con(ZFC + “there exists an inaccessible stationary limit of measurable cardinals”).We start with a discussion of the canonical functions and look at some combinatorial principles. Assuming the domination property of Theorem 1, we use the Ketonen diagram to show that ω2V is a limit of measurable cardinals in Jensen's core model KMO for measures of order zero. Using related arguments we show that ω2V is a stationary limit of measurable cardinals in KMO, if there exists a weakly normal ultrafilter on ω1. The proof yields some other results, e.g., on the consistency strength of weak*-saturated filters on ω1, which are of interest in view of the classical Ulam problem.

Lorentz-Schatten Classes and Pointwise Domination of Matrices

We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces.