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We show that a connected group interpretable in a compact complex manifold (a meromorphic group) is definably an extension of a complex torus by a linear algebraic group, generalizing results in [4]. A special case of this result, as well as one of the ingredients in the proof, is that a strongly minimal modular meromorphic group is a complex torus,… (More)

The notion of a D-ring, generalizing that of a differential or a difference ring, is introduced. Quantifier elimination and a version of the Ax-Kochen-Ershov principle is proven for a theory of valued D-fields of residual characteristic zero. The model theory of differential and difference fields has been extensively studied (see for example [7, 3]) and… (More)

We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of… (More)

Communication, i.e., moving data, between levels of a memory hierarchy or between parallel processors on a network, can greatly dominate the cost of computation, so algorithms that minimize communication can run much faster (and use less energy) than algorithms that do not. Motivated by this, attainable communication lower bounds were established in [12,… (More)

- Thomas Warren Scanlon, Thomas Scanlon, Dan Abramovic, Matthias Aschenbrenner, Brian Conrad, Keith Conrad +5 others
- 1997

In this thesis we introduce a general notion of a D-ring generalizing that of a differential or difference ring. In Chapter 3, this notion is specialized to consider valued fields D-fields: valued fields K having an operator D : K → K and a fixed element e ∈ K satisfying D(x + y) = Dx + Dy, D(1) = 0, D(xy) = xDy + yDx + eDxDy, v(e) ≥ 0, and v(Dx) ≥ v(x).… (More)

We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morley rank. § 1 consists of some general lemmas relating the… (More)

We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kähler manifold to be totally degenerate (that is, to be an indis-cernible set, in its canonical language) and point out that there are K3 surfaces which… (More)

Extending the work of [7] on groups definable in compact complex manifolds and of [1] on strongly minimal groups definable in nonstandard compact complex man-ifolds, we classify all groups definable in nonstandard compact complex manifolds showing that if G is such a group then there are a linear algebraic group L, a definably compact group T , and… (More)