Subject / 8 records

Model theory and definability

Arithmetic interpretation, types, homogeneity, definability, and first-order classification.

Classification: Second Brain

8 records

• 10.5281/zenodo.234699552026

  Order, norming faces, and symmetries of Tursi's Banach lattice

  Martino Lupini · Orderability, Groups

  Let L be Tursi’s separable universal homogeneous real Banach lattice. The set of decreasing positive sequences with infimum zero is coanalytic complete, even for sequences of components of one fixed quasi-interior vector, providing a fixed-lattice coanalytic-complete example for the decreasing-order-complexity question raised in Tursi’s 2024 survey. This gives a negative answer to the 2024 question of Avilés, Rosendal, Taylor, and Tradacete whether every separable Banach lattice belongs to their countable Fatou hierarchy. Unrestricted sequential order convergence has the exact complete complexity coA(Pi^1_1), the dual of one Souslin operation on coanalytic sets. We classify quasi-interior positive vectors by their norming Choquet simplices and answer Tursi’s documented 2021 automorphism-group universality question affirmatively. We prove universality of embedding orbits for every nonzero separable domain and of automorphism conjugacy, and establish concentration, lifting, and representation results for pointwise face kernels. Further results describe generic embedding orbits, ideals, and finite-dimensional approximate disposition.

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• 10.5281/zenodo.234527882026

  The small index property for the random poset

  Martino Lupini · Posets, Descriptive set theory, Groups

  Let P be the countable universal homogeneous poset. We prove that every abstract subgroup H ≤ Aut(P) with [Aut(P):H] < 2^{ℵ₀} contains the pointwise stabilizer of a finite subset of P. Thus Aut(P) has the small index property, answering the question recorded as open by Barbina and Macpherson in 2005. No regularity assumption on H is required. The proof equips P with a generic strictly increasing rational-valued rank. Its stabilizer has ample generics, and generic pairs of ranks yield a comeager double coset. We show that the small index property passes from a closed subgroup with such a double coset to the ambient Polish group.

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• 10.5281/zenodo.234044292026

  Spectral ranks and dynamical lengths of preliminary C*-algebras

  Martino Lupini · C*-algebras, Descriptive set theory

  We classify the spectral ranks and automorphism lengths of nonzero separable preliminary C*-algebras, whose irreducible representations are all finite-dimensional. The spectral invariants are the Fell rank ρ and the Pedersen rank β of the irreducible-dimension function. Automorphism length q measures the transfinite descriptive complexity of automorphisms modulo those implemented by multiplier unitaries; its fractional values distinguish terminal Borel classes.

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• 10.5281/zenodo.232914432026

  Arithmetic denominators and ordinary compact orbit comparisons

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 10.5281/zenodo.232847082026

  A three-generated abelian lattice-ordered group without an existentially closed prime extension

  Martino Lupini · Orderability, Groups

  No abstract on this deposit.

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• 10.5281/zenodo.229237112026

  Norm formulas, independence, and spaces of types

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 10.5281/zenodo.228906182026

  Rosenthal representations of homogeneous spaces: rank-one classifications and higher-rank criteria

  Martino Lupini · Mathematics

  No abstract on this deposit.

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• 10.5281/zenodo.226918402026

  Homogeneity of complete M-faces of the noncommutative Poulsen simplex

  Martino Lupini · Mathematics

  No abstract on this deposit.

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