IJPAM: Volume 101, No. 2 (2015)

DOWNSETS AND
GENERALIZED DESCRIPTIVE SET THEORY

Martin Dowd
1613 Wintergreen Pl.
Costa Mesa, CA 92626, USA


Abstract. Downsets over a regular cardinal $\kappa$ arise from $\Pi^1_1$ normal form. For inaccessible $\kappa$ downsets correspond to the trees of generalized descriptive set theory. Basic properties of downsets, trees, and the correspondence are considered. A new characterization of weak compactness is given. Some facts about $\Sigma^1_1$ WPS's are proved.

Received: February 2, 2015

AMS Subject Classification: 03E55

Key Words and Phrases: $\Pi_1^1$ normal form, generalized Baire space

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DOI: 10.12732/ijpam.v101i2.15 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 2
Pages: 305 - 324


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