In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality
which contains no subset order-isomorphic to
with the usual ordering
the reverse of
an uncountable subset of the Real numbers with the usual ordering.
Unlike Suslin lines, the existence of Aronszajn lines is provable using the standard axioms of set theory. A linear ordering is an Aronszajn line if and only if it is the lexicographical ordering of some Aronszajn tree.[1]
^Funk, Will; Lutzer, David J. (2005). "Lexicographically ordered trees". Topology and Its Applications. 152 (3): 275–300. doi:10.1016/j.topol.2004.10.011. Zbl 1071.03032.
In mathematical set theory, an Aronszajnline (named after Nachman Aronszajn) is a linear ordering of cardinality ℵ 1 {\displaystyle \aleph _{1}} which...
Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn...
Shelah. Shelah also conjectured that, assuming PFA, every Aronszajnline contains a Countryman line. This conjecture, which remained open for three decades...
Nachman Aronszajn (26 July 1907 – 5 February 1980) was a Polish American mathematician. Aronszajn's main field of study was mathematical analysis, where...
embeddings of the space into larger spaces. However it is a theorem of Aronszajn & Panitchpakdi (1956) that these two different types of definitions are...
He is known for the Aronszajn–Cordes uniqueness theorem for solutions of elliptic PDEs (due independently to Nachman Aronszajn). At the University of...
diamond principle ◊ proves the existence of a Suslin line, while MA + ¬CH implies EATS (every Aronszajn tree is special), which in turn implies (but is not...
called Aronszajn spaces, Gagliardo spaces or Slobodeckij spaces, after the names of the mathematicians who introduced them in the 1950s: N. Aronszajn ("Boundary...
can be combined to provide the simple factorization By the Weinstein–Aronszajn identity, one of the two matrices in the block-diagonal matrix is invertible...
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...
Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa...
Over the course of 15 years Dixmier, aided by a suggestion of Nachman Aronszajn and inequalities proved by Joseph Hersch, developed an example of a non-trivial...
Cobos, Fernando; Peetre, Jaak (1989). "Interpolation of compactness using Aronszajn-Gagliardo functors". Israel Journal of Mathematics. 68 (2): 220–240. doi:10...
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