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On a question of Andreas Weiermann
Author(s) -
Kotlarski Henryk,
Zdanowski Konrad
Publication year - 2009
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710089
Subject(s) - mathematics , existential quantification , mathematical economics , combinatorics , calculus (dental) , discrete mathematics , medicine , dentistry
We prove that for each β , γ < ε 0 there exists α < ε 0 such that whenever A ⊆ ω is α ‐large and G : A → β is such that (∀ a ∈ A )(psn( G ( a )) ≤ a ), then there exists a γ ‐large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ω ω ω(© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)