Mathematical Logic Quarterly 43 (1):121-133 (1997)
AbstractThis paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic
Similar books and articles
Analytic Combinatorics, Proof-Theoretic Ordinals, and Phase Transitions for Independence Results.Andreas Weiermann - 2005 - Annals of Pure and Applied Logic 136 (1):189-218.
A Covering Lemma for HOD of K (ℝ).Daniel W. Cunningham - 2010 - Notre Dame Journal of Formal Logic 51 (4):427-442.
Combinatorics and Graph Theory.John Harris, Jeffry L. Hirst & Michael Mossinghoff - 2008 - Springer.
Semi-Monotone Series of Ordinals.John L. Hickman - 1979 - Notre Dame Journal of Formal Logic 20 (1):196-200.
Some Recent Developments in Higher Recursion Theory.Sy D. Friedman - 1983 - Journal of Symbolic Logic 48 (3):629-642.
Full Reflection of Stationary Sets Below ℵω.Thomas Jech & Saharon Shelah - 1990 - Journal of Symbolic Logic 55 (2):822 - 830.
Combinatorics on Ideals and Axiom A.James D. Sharp - 1994 - Journal of Symbolic Logic 59 (3):997-1000.
Intermediate Predicate Logics Determined by Ordinals.Pierluigi Minari, Mitio Takano & Hiroakira Ono - 1990 - Journal of Symbolic Logic 55 (3):1099-1124.
Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.
Order Types of Ordinals in Models of Set Theory.John E. Hutchinson - 1976 - Journal of Symbolic Logic 41 (2):489-502.
On Topological Spaces Equivalent to Ordinals.Jörg Flum & Juan Carlos Martinez - 1988 - Journal of Symbolic Logic 53 (3):785-795.
A Functorial Property of the Aczel-Buchholz-Feferman Function.Andreas Weiermann - 1994 - Journal of Symbolic Logic 59 (3):945-955.
Added to PP
Historical graph of downloads
Citations of this work
2001–2002 Winter Meeting of the Association for Symbolic Logic.Greg Hjorth - 2002 - Bulletin of Symbolic Logic 8 (2):312-318.
References found in this work
No references found.