Stronger Forms of Determinacy
Several set-theoretic principles about determinacy stronger than Borel determinacy are studied in descriptive set theory. They are closely related to large cardinal axioms.
The axiom of projective determinacy states that all projective subsets of a Polish space are determined. It is known to be unprovable in ZFC but relatively consistent with it and implied by certain large cardinal axioms. The existence of a measurable cardinal is enough to imply over ZFC that all analytic subsets of Polish spaces are determined.
The axiom of determinacy states that all subsets of all Polish spaces are determined. It is inconsistent with ZFC but equiconsistent with certain large cardinal axioms.
Read more about this topic: Borel Determinacy Theorem
Famous quotes containing the words stronger and/or forms:
“She fair, divinely fair, fit love for Gods,
Not terrible, though terror be in love,
And beauty, not approached by stronger hate,
Hate stronger under show of love well feigned—
The way which to her ruin now I tend.””
—John Milton (1608–1674)
“Three forms I see on stretchers lying, brought out there untended
lying,
Over each the blanket spread, ample brownish woolen blanket,
Gray and heavy blanket, folding, covering all.”
—Walt Whitman (1819–1892)