Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only… (More)

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional… (More)

Assuming some large cardinals, a model of ZFC is obtained in which אω+1 carries no Aronszajn trees. It is also shown that if λ is a singular limit of strongly compact cardinals, then λ carries no… (More)

In this paper we consider whether L(R) has “enough information” to contain a counterexample to the continuum hypothesis. We believe this question provides deep insight into the difficulties… (More)

In this paper we explicate a very weak version of the principle discovered by Jensen who proved it holds in the constructible universe L. This principle is strong enough to include many of the known… (More)

Suppose a knowledge base contains information on how the world generally behaves and in particular contains the information that birds, normally fly. Suppose that we obtain the information that… (More)

There have been numerous results showing that a measurable cardinal κ can carry exactly α normal measures in a model of GCH, where α is a cardinal at most κ++. Starting with just one measurable… (More)

We start by studying the relationship between two invariants isolated by Shelah, the sets of good and approachable points. As part of our study of these invariants, we prove a form of “singular… (More)