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- Jakub Gismatullin, Davide Penazzi, Anand Pillay
- Ann. Pure Appl. Logic
- 2014

For G a group definable in some structure M , we define notions of “definable” compactification of G and “definable” action of G on a compact space X (definable G-flow), where the latter is under a definability of types assumption on M . We describe the universal definable compactification of G as G∗/(G∗)00 M and the universal definable G-ambit as the type… (More)

- Davide Penazzi, M. R. VALLUZZI, A. SAISI, Luca Binda, C. Modena
- 2001

The 1997 Umbria Marche earthquake offered a unique opportunity to verify the knowledge on seismic response and on retrofitting strategies of historic masonry structures which have been developed during the last twenty years. Severe damages were in fact suffered also by those buildings that had already been, and in some cases were still being, repaired and… (More)

We study the action of G = SL(2,R), viewed as a group definable in the structure M = (R,+,×), on its type space SG(M). We identify a minimal closed G-flow I, and an idempotent r ∈ I (with respect to the Ellis semigroup structure ∗ on SG(M)). We also show that the “ideal group” (r ∗ I, ∗) is nontrivial (in fact it will be the group with 2 elements), yielding… (More)

- Davide Penazzi
- 2003

In [1] the Furstenberg Structure Theorem for flows was extended from the metric to the non-metric case by means of a special construction of minimal flows. We are able to use this construction to generalize another theorem from the metric to the non-metric case: Glasner proved in [4] that if the space of regular Borel probability measures of a flow is… (More)

- Davide Penazzi
- Arch. Math. Log.
- 2011

We initiate a geometric stability study of groups of the form G/G, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M . We consider an enriched structure M ′ with a predicate for G and prove 1-basedness for additive truncations of M , multiplicative truncations, SO2(M) and its truncations; such groups… (More)

- Gareth Boxall, David Bradley-Williams, Charlotte Kestner, Alexandra Omar Aziz, Davide Penazzi
- Notre Dame Journal of Formal Logic
- 2013

We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based with respect to þ-independence. We also study geometries… (More)

- Davide Penazzi
- 2010

We proceed with an analysis of 1-basedness for bounded hyperdefinable groups of the form G/G where G = E(K) is the semialgebraic connected component of the K-points of an elliptic curve over a saturated real closed field K, or G a truncation of E(K); we follow the method developed in [1]. We then relate the map G→ G/G with the algebraic geometric notion of… (More)

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