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Trees, subtrees and order types

Stevo B. Todorčević

Annals of Mathematical Logic 20 (3):233 (1981)

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Square with built-in diamond-plus.Assaf Rinot & Ralf Schindler - 2017 - Journal of Symbolic Logic 82 (3):809-833.details We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds inLfor every infinite cardinal.As an application, we prove that the following two hold inL:1.For every infinite regular cardinalλ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinalλ, there exists arespectingλ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed inL. Download Export citation Bookmark 1 citation
A microscopic approach to Souslin-tree constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.details Download Export citation Bookmark 6 citations
Some higher-gap examples in combinatorial set theory.A. Hajnal & P. Komjáth - 1987 - Annals of Pure and Applied Logic 33 (C):283-296.details Download Export citation Bookmark
Local coherence.Bernhard König - 2003 - Annals of Pure and Applied Logic 124 (1-3):107-139.details We characterize the tree of functions with finite support in terms of definability. This turns out to have various applications: a new kind of tree dichotomy for ω1 on the one hand. On the other hand, we prove a reflection principle for trees on ω2 under SPFA. This reflection of trees implies stationary reflection. Download Export citation Bookmark 2 citations
Morasses, square and forcing axioms.Charles Morgan - 1996 - Annals of Pure and Applied Logic 80 (2):139-163.details The paper discusses various relationships between the concepts mentioned in the title. In Section 1 Todorcevic functions are shown to arise from both morasses and square. In Section 2 the theme is of supplements to morasses which have some of the flavour of square. Distinctions are drawn between differing concepts. In Section 3 forcing axioms related to the ideas in Section 2 are discussed. Download Export citation Bookmark 4 citations
Semimorasses and nonreflection at singular cardinals.Piotr Koszmider - 1995 - Annals of Pure and Applied Logic 72 (1):1-23.details Some subfamilies of κ, for κ regular, κ λ, called -semimorasses are investigated. For λ = κ+, they constitute weak versions of Velleman's simplified -morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of -morasses with this difference that the obtained objects are of size λ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve existence of nonreflecting objects of singular (...) Download Export citation Bookmark 6 citations
Simplified morasses with linear limits.Dan Velleman - 1984 - Journal of Symbolic Logic 49 (4):1001-1021.details Download Export citation Bookmark 6 citations
Notes on some erdős–hajnal problems.Péter Komjáth - 2021 - Journal of Symbolic Logic 86 (3):1116-1123.details We make comments on some problems Erdős and Hajnal posed in their famous problem list. Let X be a graph on $\omega _1$ with the property that every uncountable set A of vertices contains a finite set s such that each element of $A-s$ is joined to one of the elements of s. Does then X contain an uncountable clique? We prove that both the statement and its negation are consistent. Do there exist circuitfree graphs $\{X_n:n<\omega \}$ on $\omega _1$ (...) Download Export citation Bookmark

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