Isomorphism types of Aronszajn trees

DOI10.1007/BF02761119zbMath0566.03032MaRDI QIDQ1059070

Saharon Shelah, Uri Abraham

Publication date: 1985

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

continuum hypothesisindependence resultsdiamondorder typemodels of set theoryproper forcingAronszajn treesSouslin treesclosed unbounded sets

Mathematics Subject Classification ID

Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05)

Related Items (25)

Some results on non-club isomorphic Aronszajn trees ⋮ Can a small forcing create Kurepa trees ⋮ Strong measure zero sets without Cohen reals ⋮ Club stationary reflection and the special Aronszajn tree property ⋮ Continuous images of closed sets in generalized Baire spaces ⋮ Fraïssé sequences: category-theoretic approach to universal homogeneous structures ⋮ Club degrees of rigidity and almost Kurepa trees ⋮ What makes the continuum ℵ₂ ⋮ A direct proof of the five element basis theorem ⋮ A large pairwise far family of Aronszajn trees ⋮ Souslin algebra embeddings ⋮ On minimal non-\(\sigma\)-scattered linear orders ⋮ A fragment of Asperó–Mota’s finitely proper forcing axiom and entangled sets of reals ⋮ Bounding the consistency strength of a five element linear basis ⋮ \(\omega_1\) and \(-\omega_1\) may be the only minimal uncountable linear orders ⋮ On the complexity of classes of uncountable structures: trees on $\aleph _1$ ⋮ A \({\Delta{}}^ 2_ 2\) well-order of the reals and incompactness of \(L(Q^{MM})\) ⋮ Club isomorphisms on higher Aronszajn trees ⋮ A NEW MINIMAL NON-σ-SCATTERED LINEAR ORDER ⋮ Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders ⋮ Degrees of rigidity for Souslin trees ⋮ Chain homogeneous Souslin algebras ⋮ Galvin's question on non-\( \sigma \)-well ordered linear orders ⋮ A model with Suslin trees but no minimal uncountable linear orders other than \(\omega_1\) and \(- \omega_1\) ⋮ Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)

Cites Work

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• On the consistency of some partition theorems for continuous colorings, and the structure of \(\aleph _ 1\)-dense real order types
• Martin's axiom does not imply that every two \(chi_ 1-\)dense sets of reals are isomorphic
• Proper forcing
• Decomposing uncountable squares to countably many chains
• Classification theory and the number of non-isomorphic models
• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
• The Souslin problem
• Some counterexamples in the partition calculus
• Forcing with stable posets
• On the standard part of nonstandard models of set theory
• Construction of a Rigid Aronszajn Tree
• Αll $ℵ_1$-dense sets of reals can be isomorphic
• Isomorphism Types of Trees

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