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49
An Aronszajn Tree
"... Contrary to the popular belief that “infinity is not a number; it’s a concept, ” numbers that are not fi-nite do exist. Mathematicians call them transfinite numbers. Just like ordinary numbers, some trans-finite numbers are larger than others. This can be thought of as there being different levels o ..."
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of infinity, where some infinities are “more infinite ” than oth-ers. If we draw a family tree in which every gener-ation has finitely many offspring, and every chain of descendants is finite, then it is clear that we can-not have infinitely many family members. In the realm of the transfinite, things
STRUCTURAL ANALYSIS OF ARONSZAJN TREES
"... Abstract. In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, subtree bases for Aronszajn trees, and the existence of minimal Aronszajn types. 1. ..."
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Cited by 4 (2 self)
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Abstract. In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, subtree bases for Aronszajn trees, and the existence of minimal Aronszajn types. 1.
SPECIALISING ARONSZAJN TREES BY COUNTABLE APPROXIMATIONS
"... Abstract. We show that there are proper forcings based upon countable trees of creatures that specialise a given Aronszajn tree. 778 revision:2002-05-27 modified:2002-07-16 The main point of this work is finding forcing notions specialising an Aronszajn tree, which are creature forcings, tree-like w ..."
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Abstract. We show that there are proper forcings based upon countable trees of creatures that specialise a given Aronszajn tree. 778 revision:2002-05-27 modified:2002-07-16 The main point of this work is finding forcing notions specialising an Aronszajn tree, which are creature forcings, tree
SPECIALIZING ARONSZAJN TREES BY COUNTABLE APPROXIMATIONS
, 2001
"... Abstract. We show that there are proper forcings based upon countable trees of creatures that specialize a given Aronszajn tree. The main point of this work is finding forcing notions specializing an Aronszajn tree, which are creature forcings, tree-like with halving, but being based on ω1 (the tree ..."
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Cited by 2 (0 self)
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Abstract. We show that there are proper forcings based upon countable trees of creatures that specialize a given Aronszajn tree. The main point of this work is finding forcing notions specializing an Aronszajn tree, which are creature forcings, tree-like with halving, but being based on ω1 (the
Aronszajn Trees and the SCH
, 2009
"... These are notes on results presented by Itay Neeman at the Appalachian ..."
SPECIALISING ALL ARONSZAJN TREES AND ESTABLISHING THE OSTASZEWSKI CLUB
"... principle imply the existence of a Souslin tree? We consider proper forcings based upon countable trees of creatures that specialise a given Aronszajn tree and iterate these forcings with countable support. We prove that the Ostaszewki club holds in the extension. We work with notions specialising a ..."
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principle imply the existence of a Souslin tree? We consider proper forcings based upon countable trees of creatures that specialise a given Aronszajn tree and iterate these forcings with countable support. We prove that the Ostaszewki club holds in the extension. We work with notions specialising
Extender based forcings, fresh sets and Aronszajn trees
, 2011
"... Extender based forcings are studied with respect of adding branches to Aronszajn trees. We construct a model with no Aronszajn tree over ℵω+2 from the optimal assumptions. This answers a question of Friedman and Halilovic ́ [1]. The reader interested only in Friedman and Halilovic ́ question may ski ..."
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Cited by 1 (0 self)
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Extender based forcings are studied with respect of adding branches to Aronszajn trees. We construct a model with no Aronszajn tree over ℵω+2 from the optimal assumptions. This answers a question of Friedman and Halilovic ́ [1]. The reader interested only in Friedman and Halilovic ́ question may
Aronszajn trees and failure of the singular cardinal hypothesis
- J. Math. Log
"... Abstract. The tree property at κ + states that there are no Aronszajn trees on κ +, or, equivalently, that every κ + tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ + and failure of the singular cardinal hypothesis at κ; the former is ..."
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Cited by 13 (3 self)
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Abstract. The tree property at κ + states that there are no Aronszajn trees on κ +, or, equivalently, that every κ + tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ + and failure of the singular cardinal hypothesis at κ; the former
SPECIALISING ARONSZAJN TREES AND PRESERVING SOME WEAK DIAMONDS
"... Abstract. We show that ♦(R, N, ∈) together with CH and “all Aronszajn trees are special ” is consistent relative to ZFC. The weak diamond for the covering relation of Lebesgue null sets was the only weak diamond in the Cichoń diagramme for relations whose consistency together with “all Aronszajn tre ..."
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Abstract. We show that ♦(R, N, ∈) together with CH and “all Aronszajn trees are special ” is consistent relative to ZFC. The weak diamond for the covering relation of Lebesgue null sets was the only weak diamond in the Cichoń diagramme for relations whose consistency together with “all Aronszajn
Results 1 - 10
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49
