More on lower bounds for partitioning α-large sets

Annals of Pure and Applied Logic 147 (3):113-126 (2007)
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Abstract

Continuing the earlier research from [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001] we show that for the price of multiplying the number of parts by 3 we may construct partitions all of whose homogeneous sets are much smaller than in [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001]. We also show that the Paris–Harrington independent statement remains unprovable if the number of colors is restricted to 2, in fact, the statement is unprovable in IΣb. Other results concern some lower bounds for partitions of pairs

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Citations of this work

Phase transitions for Gödel incompleteness.Andreas Weiermann - 2009 - Annals of Pure and Applied Logic 157 (2-3):281-296.
On a question of Andreas Weiermann.Henryk Kotlarski & Konrad Zdanowski - 2009 - Mathematical Logic Quarterly 55 (2):201-211.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
A mathematical incompleteness in Peano arithmetic.Jeff Paris & Leo Harrington - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 90--1133.
Transfinite induction within Peano arithmetic.Richard Sommer - 1995 - Annals of Pure and Applied Logic 76 (3):231-289.

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