On the question of absolute undecidability

In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Philosophia Mathematica. Association for Symbolic Logic 153-188 (2010)
The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH and that there is not currently a convincing case to the effect that a given statement is absolutely undecidable
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DOI 10.1093/philmat/nkj009
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Peter Koellner (2009). On Reflection Principles. Annals of Pure and Applied Logic 157 (2):206-219.
Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.

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