Regressive partition relations, n-subtle cardinals, and Borel diagonalization

Annals of Pure and Applied Logic 52 (1-2):65-77 (1991)
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Abstract

We consider natural strengthenings of H. Friedman's Borel diagonalization propositions and characterize their consistency strengths in terms of the n -subtle cardinals. After providing a systematic survey of regressive partition relations and their use in recent independence results, we characterize n -subtlety in terms of such relations requiring only a finite homogeneous set, and then apply this characterization to extend previous arguments to handle the new Borel diagonalization propositions

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10.1016/0168-0072(91)90039-o

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Akihiro Kanamori
Boston University

Citations of this work

Subtlety and partition relations.Toshimichi Usuba - 2016 - Mathematical Logic Quarterly 62 (1-2):59-71.

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References found in this work

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.
On Gödel incompleteness and finite combinatorics.Akihiro Kanamori & Kenneth McAloon - 1987 - Annals of Pure and Applied Logic 33 (C):23-41.
Regressive partitions and borel diagonalization.Akihiro Kanamori - 1989 - Journal of Symbolic Logic 54 (2):540-552.

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