We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX ×OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with ...

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“Microbiology Topics” discusses various topics in microbiology of practical use in validation and compliance. We intend this column to be a useful resource for daily work applications. Reader comments, questions, and suggestions are needed to help us fulfill our objective for this column. Please send your comments and suggestions to column coordinator Scott Sutton at scott. [email protected]...

There exists a countable structure M of Scott rank ωCK 1 where ωM 1 = ω CK 1 and where the LωCK 1 ,ω-theory of M is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its Lωβ,ω-theory. Most well-known models with unbounded atoms below ωCK 1 also realize a non-principal LωCK 1 ,ω-type; such a model that preserves the Σ1-admissibility of ωCK 1 will hav...

Consumers have rarely known the price of medical care before receiving it, but access to price information is becoming more common. For a group of consumers with access to price information, I use detailed data on search, health care use, and negotiated prices to show that search leads consumers to pay significantly lower prices. I provide suggestive evidence that insurance coverage inhibits th...

We give a new definition of Scott rank motivated by our main theorem: For every countable structure A and ordinal α < ω1, we have that: every automorphism orbit is Σ α -definable without parameters if and only if A has a Π α+1 Scott sentence, if and only if A is uniformly boldface ∆α-categorical. As a corollary, we show that a structure is computably categorical on a cone if and only if it is t...

New results in the representation theory of “semisimple” algebraic monoids are obtained, based on Renner’s monoid version of Chevalley’s big cell. (The semisimple algebraic monoids have been classified by Renner.) The rational representations of such a monoid are the same thing as “polynomial” representations of the associated reductive group of units in the monoid, and this representation cate...