Annals of Pure and Applied Logic 54 (3):265-291 (1991)

Abstract
We study the provability in subsystems of second-order arithmetic of two theorems of Harrington and Shelah [6] about Borel quasi-orderings of the reals. These theorems turn out to be provable in ATR0, thus giving further evidence to the observation that ATR0 is the minimal subsystem of second-order arithmetic in which significant portion of descriptive set theory can be developed. As in [6] considering the lightface versions of the theorems will be instrumental in their proof and the main techniques employed will be the reflection principles and Gandy forcing
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DOI 10.1016/0168-0072(91)90050-v
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References found in this work BETA

Countable Algebra and Set Existence Axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Weak Axioms of Determinacy and Subsystems of Analysis II.Kazuyuki Tanaka - 1991 - Annals of Pure and Applied Logic 52 (1-2):181-193.
The Galvin-Prikry Theorem and Set Existen Axioms.Kazuyuki Tanaka - 1989 - Annals of Pure and Applied Logic 42 (1):81-104.
The Metamathematics of Scattered Linear Orderings.P. Clote - 1989 - Archive for Mathematical Logic 29 (1):9-20.

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