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To logicians, arithmetic is horribly complicated. 1) is undecidable. Moreover, there are sets defined by arbitrarily complicated formulae (in the sense of quantifier complexity, say) which cannot be expressed in terms of simpler formulae. On the contary, geometry is very regular. Theorem 2 (Tarski) Euclidean geometry, understood as the theory of the real(More)
The following propositions seem both plausible in their own right and apparently inconsistent: (1) Moral judgements like 'It is right that I V' ('valuations' for short) express beliefs; in this case, a belief about the rightness of my D-ing. (2) There is some sort of a necessary connection between being in the state thejudgement 'It is right that I '(More)
Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination and stability result for finitely generated modules over certain finite simple extensions of the integers given together with predicates for cycles of the distinguished generator 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)
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)