Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn...

such trees are known as Aronszajn trees. Given a cardinal number κ {\displaystyle \kappa } , a κ {\displaystyle \kappa } -Suslin tree is a tree of height...

In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality ℵ 1 {\displaystyle \aleph _{1}} which...

after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the...

(MA); MA + ¬CH (independence shown by Solovay and Tennenbaum). Every Aronszajn tree is special (EATS); We have the following chains of implications: V =...

T. Smith, Aronszajn offered proof of the Aronszajn–Smith theorem. Also, the existence of Aronszajn trees was proven by Aronszajn; Aronszajn lines, also...

MR 2270949. Diestel, Reinhard; Leader, Imre (2001), "Normal spanning trees, Aronszajn trees and excluded minors" (PDF), Journal of the London Mathematical Society...

collapsing ℵ1, and results in a tree with exactly ℵ1 branches. Aronszajn tree Suslin tree Jech, Thomas J. (1971), "Trees", Journal of Symbolic Logic, 36:...

can be defined by first-order formulas Aronszajn 1.  Nachman Aronszajn 2.  An Aronszajn tree is an uncountable tree such that all branches and levels are...

_{2}} -Aronszajn trees is equiconsistent with the existence of a Mahlo cardinal, the non-existence of ω 2 {\displaystyle \omega _{2}} -Aronszajn trees is...

using the finite intersection property characterization of compactness. Aronszajn tree, for the possible existence of counterexamples when generalizing the...

Schlindwein, C., "Consistency of Suslin's hypothesis, a non-special Aronszajn tree, and GCH", (1994), Journal of Symbolic Logic (59) pp. 1–29 Jech, Thomas...

EATS may refer to: Empire Air Training Scheme Every Aronszajn tree is special EAT (disambiguation) This disambiguation page lists articles associated with...

includes the partition calculus of Paul Erdős and Richard Rado, trees and Aronszajn trees, the model-theoretic study of large cardinals, and the existence...

Hypothesis. In 1980, Todorčević and Abraham proved the existence of rigid Aronszajn trees and the consistency of MA + the negation of the continuum hypothesis...

embeddings of the space into larger spaces. However it is a theorem of Aronszajn & Panitchpakdi (1956) that these two different types of definitions are...

theorem (functional analysis) Milman–Pettis theorem (Banach space) Moore–Aronszajn theorem (Hilbert space) Orlicz–Pettis theorem (functional analysis) Quotient...

Martinez-Ranero has proven that, under the proper forcing axiom, the class of Aronszajn lines is better-quasi-ordered under the embeddability relation. It is...

several theorems that he did not find time to publish. He told Nachman Aronszajn and K. T. Smith that in the early 1930s he proved the existence of proper...

Nachman Aronszajn, Polish-American Michel Balinski, American-French Stefan Banach Tadeusz Banachiewicz Kazimierz Bartel Andrzej Białynicki-Birula Karol...