UNIVERSAL THEORIES AND COMPACTLY EXPANDABLE MODELS

Saturated models of universal theories

A notion called Herbrand saturation is shown to provide the modeltheoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

Centralization and decentralization: Theories and Models

The questions of centralization and decentralization arise in every polity. The constitution or the practice or both have to settle how much of policy making is to be decided by the central government and by component bodies. By and large liberalism and decentralization tend to go together while authoritarianism tends to be associated with centralization. The constitutional model which is gener...

Universal Homotopy Theories

Model categories were introduced by Quillen [Q] to provide a framework through which one could apply homotopy theory in various settings. They have been astonishingly successful in this regard, and in recent years one of the first things one does when studying any homotopical situation is to try to set up a model structure. The aim of this paper is to introduce a new, but very basic, tool into ...

On universal theories of defaults

Though unifications of some of the numerous theories of default reasoning have been found, we add to doubts about the existence of universal theories by viewing default reasoning from the standpoint of decision theory as a case of rational self-government of inference. Default rules express not only methods for deriving new conclusions from old, but also preferences among sets of possible concl...

Universal Unification and Regular Equational ACFM Theories