User:Trovatore/Tasks

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• Axiom of dependent choice and Transfinite induction -- check my facts on sequences of countable length.
• L(R) -- check my facts re Wadge degree of R#. Define "definable powerset" (but maybe in the L article).
• Infinity-Borel set -- Fix definition! Something about ∞-Borel codes, characterization in terms of set of all x such that for some set of ordinals S.
  • DONE.
• Fill out Borel equivalence relation according to plans in the talk page
• Sort out merge between Inaccessible cardinal and Strongly inaccessible cardinal
  • Done (could still use some cleanup).
• Improve Axiom of determinacy page. Possibly start a Game (determinacy theory) page or some such.
• Create Pointclass page.
• Create Scale property page.
• Expand Uniformization (set theory) page -- add applications.
• Address misconceptions/formalist bias in Axiomatic set theory, Naive set theory, [[Category:Set theory]].
  • (Waiting for responses to related issue in Russell paradox)
• Address lightface/boldface confusion in Analytical hierarchy. Define lightface pointclasses only for Cantor and Baire space, or try to do it for any Polish space together with a fixed countable base?
• Address set/formula confusion both in Analytical hierarchy and in Arithmetical hierarchy.
• Definition of height in Tree (set theory). Maybe give both definitions and say they're equivalent.
• Add section for Σ²₁ definition of Continuum hypothesis. Point out that it's simpler than the definition given at the top of the argument (which call "weak CH"), equivalent given AC, but AD implies weak CH but refutes CH. CH relativizes up between models having same reals.
• Get some sort of uniformity between property of Baire, perfect set property, and measurable set. Mention universal measurability in the last? It's currently a redirect; write article? Maybe instead it should be an article on universally measurable.
• Article on regularity properties subsuming the above three?
  • Added list of properties of sets of reals, but still, the above might not be a bad idea.
• Create Universally Baire set page.
• Create Structure (mathematical logic) page? Some overlap with model theory, but the latter should really discuss the things that are actually called model theory (stability, saturation, homogeneity, etc) rather than Tarskian structures and semantics.