1,720,982 research outputs found
Arithmetic of Dedekind cuts of ordered Abelian groups
No full textAbstractWe study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures
o-Minimal cohomology: Finiteness and Invariance Results
No full textThe topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language
The addition theorem for locally monotileable monoid actions
Get PDFWe prove an instance of the so-called Addition Theorem for the algebraic entropy of actions of cancellative right amenable monoids S on discrete abelian groups A by endomorphisms, under the hypothesis that S is locally monotileable (that is, S admits a right Følner sequence (Fn)n∈N such that Fn is a monotile of Fn+1 for every n∈N). We study in details the class of locally monotileable groups, also in relation with already existing notions of monotileability for groups, introduced by B. Weiss and developed further by other authors recently
Embedding Henselian fields into power series
No full textAbstractEvery Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain the Ax–Kochen–Ershov theorem and an extension of Mourgues and Ressayre's theorem: every ordered field which is Henselian in its natural valuation has an integer part. We also give some results for the mixed and the finite characteristic cases
Towers of complements to valuation rings and truncation closed embeddings of valued fields
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