Abstract. We extend Shelah’s first many model result to show that an unstable theory has 2κ many non-permutation group isomorphic models of size κ, where κ is an uncountable ...
Abstract. We extend Morley's Theorem to show that if a theory is -pcategorical for some uncountable cardinal , it is uncountably categorical. We then discuss -p-categoriticy a...
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
An uncovering-by-bases for a group G acting on a finite set is a set U of bases for G such that any r-subset of is disjoint from at least one base in U, where r is a parameter d...
We study the random composition of a small family of O(n3 ) simple permutations on {0, 1}n . Specifically we ask how many randomly selected simple permutations need be composed to...