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Descriptive set theoretical complexity of randomness notions

100%

Yu L.

Fundamenta Mathematicae

2011

tom 215

nr 3

219-231

We study the descriptive set theoretical complexity of various randomness notions.

The strength of the projective Martin conjecture

51%

Chong C., Wang W., Yu L.

Fundamenta Mathematicae

2010

tom 207

nr 1

21-27

We show that Martin's conjecture on Π¹₁ functions uniformly $≤_T$-order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant $Π¹_{2n+1}$ functions is equivalent over ZFC to $Σ¹_{2n+2}$-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Yu L.

1 Chong C.

1 Wang W.

1 2011

1 2010

Wyniki wyszukiwania

Descriptive set theoretical complexity of randomness notions

The strength of the projective Martin conjecture