Kanamori's 'The Higher Infinite' establishes that weak compactness is a Π¹₁-indescribability property, and indescribability does not by itself generate κ-many inaccessible predecessors without additional large cardinal axioms.
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A branch of mathematics that studies collections of objects (called 'sets') and the rules for how they relate to each other.
Weak compactness(mathematical property being discussed)
A property of very large numbers (called cardinals) in set theory that describes a kind of logical strength or 'completeness' they possess.
Π¹₁-indescribability(property classification)
A technical measure of how 'large' or 'powerful' a number is in set theory—basically, it describes a specific way a number cannot be fully captured by certain logical statements.
κ (kappa)(mathematical notation)
A symbol used in set theory to represent a large cardinal number (roughly: a really, really big number with special properties).