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Local analysis for semi-bounded groups

Pantelis E. Eleftheriou (2012)

Fundamenta Mathematicae

An o-minimal expansion ℳ = ⟨M,<,+,0, ...⟩ of an ordered group is called semi-bounded if it does not expand a real closed field. Possibly, it defines a real closed field with bounded domain I ⊆ M. Let us call a definable set short if it is in definable bijection with a definable subset of some Iⁿ, and long otherwise. Previous work by Edmundo and Peterzil provided structure theorems for definable sets with respect to the dichotomy ’bounded versus unbounded’. Peterzil (2009) conjectured a refined...

Local-global convergence, an analytic and structural approach

Jaroslav Nešetřil, Patrice Ossona de Mendez (2019)

Commentationes Mathematicae Universitatis Carolinae

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global convergence to graphs with unbounded degrees. As an application, we extend previous results on continuous clustering of local convergent sequences and prove the existence of modeling quasi-limits for local-global convergent sequences of nowhere dense graphs.

Locally compact linearly Lindelöf spaces

Kenneth Kunen (2002)

Commentationes Mathematicae Universitatis Carolinae

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.

Locally finite theories with model companion

Paolo Lipparini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dà, mediante condizioni per l'amalgamabilità di tre modelli, una caratterizzazione completa delle teorie localmente finite con model-compagno. Si introduce inoltre un concetto intermedio tra quelli di model-compagno e model-completamento.

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