Displaying similar documents to “Coherent adequate sets and forcing square”

When a first order T has limit models

Saharon Shelah (2012)

Colloquium Mathematicae

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We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.

Borel sets with large squares

Saharon Shelah (1999)

Fundamenta Mathematicae

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 For a cardinal μ we give a sufficient condition ⊕ μ (involving ranks measuring existence of independent sets) for: ⊗ μ if a Borel set B ⊆ ℝ × ℝ contains a μ-square (i.e. a set of the form A × A with |A| =μ) then it contains a 2 ℵ 0 -square and even a perfect square, and also for ⊗ μ ' if ψ ∈ L ω 1 , ω has a model of cardinality μ then it has a model of cardinality continuum generated in a “nice”, “absolute” way. Assuming M A + 2 ℵ 0 > μ for transparency, those three conditions ( ⊕ μ , ⊗ μ and ⊗ μ ' ) are equivalent, and from this we...

A viewpoint on amalgamation classes

Silvia Barbina, Domenico Zambella (2010)

Commentationes Mathematicae Universitatis Carolinae

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We give a self-contained introduction to universal homogeneous models (also known as rich models) in a general context where the notion of morphism is taken as primitive. We produce an example of an amalgamation class where each connected component has a saturated rich model but the theory of the rich models is not model-complete.