Euler characteristics of categories and homotopy colimits

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Superatomic Boolean algebras constructed from strongly unbounded functions

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Investigation of the hepatitis C virus replication complex.

Formation of a membrane-associated replication complex, composed of viral proteins, replicating RNA, altered cellular membranes, and other host factors, is a hallmark of all positive-strand RNA viruses. In the case of HCV, RNA replication takes place in a likely endoplasmic reticulum-derived membrane alteration referred to as the "membranous web." In vitro transcription-translation, membrane extraction and flotation analyses, immunofluorescence microscopy, fluorescent in situ hybridization, and RNA metabolic labeling followed by confocal laser scanning microscopy have yielded insights into the structure and function of the HCV replication complex. We describe these techniques and highlight selected results.

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.

On p-optimal proof systems and logics for PTIME

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On slicewise monotone parameterized problems and optimal proof systems for TAUT

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On absoluteness of categoricity in abstract elementary classes

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Isomorphism relations on computable structures

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Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Potential isomorphism of elementary substructures of a strictly stable homogeneous model

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Strong isomorphism reductions in complexity theory

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

Consistency and optimality

Assume that the problem Qo is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T U {ConT} as the minimal extension of T proving for some algorithm that it decides Qo as fast as any algorithm B with the property that T proves that B decides Qo. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.

The non-absoluteness of model existence in uncountable cardinals for Lw1,w

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