Compactness principles at small cardinals like ω₂ are consistent from large cardinals, remain independent of several classical conjectures including Suslin's Hypothesis and Whitehead's Conjecture, and are evaluated as potential new axioms.
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Compactness for small cardinals in mathematics: principles, consequences, and limitations
Compactness principles at small cardinals like ω₂ are consistent from large cardinals, remain independent of several classical conjectures including Suslin's Hypothesis and Whitehead's Conjecture, and are evaluated as potential new axioms.