Compact measure spaces

Fremlin, D. H.

doi:10.1112/s0025579300007798

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The Logic Topology and -Metric1

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2005

2022

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Cited by 4 publications

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“…Then L A is an Archimedean Riesz space of measurable functions on M (cf. [21]). Let σ A (M) be the set of Riesz homomorphisms I : L A → R such that I(1) = 1.…”

Section: The Logic Topology and -Metricmentioning

confidence: 99%

ℵ₀‐categorical Banach spaces contain ℓp or c₀

Khanaki

2021

Mathematical Logic Qtrly

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This paper has three parts. First, we establish some of the basic model theoretic facts about M T , the Tsirelson space of Figiel and Johnson [20]. Second, using the results of the first part, we give some facts about general Banach spaces. Third, we study model-theoretic dividing lines in some Banach spaces and their theories. In particular, we show: (1) M T has the non independence property (NIP); (2) every Banach space that is ℵ 0 -categorical up to small perturbations embeds c 0 or p (1 p < ∞) almost isometrically; consequently the (continuous) first-order theory of M T does not characterize M T , up to almost isometric isomorphism.

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“…Then L A is an Archimedean Riesz space of measurable functions on M (cf. [21]). Let σ A (M) be the set of Riesz homomorphisms I : L A → R such that I(1) = 1.…”

Section: The Logic Topology and -Metricmentioning

confidence: 99%