Skip to main content
MathOverflow

Return to Question

Add tag
Source Link
Carl Mummert
Carl Mummert
  • 9.7k
  • 1
  • 46
  • 68

Who first proved there's an $\omega$-model of $WKL_0$$\mathsf{WKL}_0$ in which all sets are low?

I am trying to pin down: who first proved that $WKL_0$$\mathsf{WKL}_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem IX.2.17), one doesn't have to travel too far to get to this result when starting from the low basis theorem of Jockusch and Soare. But Simpson's typically extensive bibliographic remarks on the section in which this result is proved offer no indication of when this fact about $WKL_0$$\mathsf{WKL}_0$ was first noted. Thanks.

Who first proved there's an $\omega$-model of $WKL_0$ in which all sets are low?

I am trying to pin down: who first proved that $WKL_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem IX.2.17), one doesn't have to travel too far to get to this result when starting from the low basis theorem of Jockusch and Soare. But Simpson's typically extensive bibliographic remarks on the section in which this result is proved offer no indication of when this fact about $WKL_0$ was first noted. Thanks.

Who first proved there's an $\omega$-model of $\mathsf{WKL}_0$ in which all sets are low?

I am trying to pin down: who first proved that $\mathsf{WKL}_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem IX.2.17), one doesn't have to travel too far to get to this result when starting from the low basis theorem of Jockusch and Soare. But Simpson's typically extensive bibliographic remarks on the section in which this result is proved offer no indication of when this fact about $\mathsf{WKL}_0$ was first noted. Thanks.

Source Link
Ed Dean
Ed Dean
  • 2.3k
  • 2
  • 18
  • 32

Who first proved there's an $\omega$-model of $WKL_0$ in which all sets are low?

I am trying to pin down: who first proved that $WKL_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem IX.2.17), one doesn't have to travel too far to get to this result when starting from the low basis theorem of Jockusch and Soare. But Simpson's typically extensive bibliographic remarks on the section in which this result is proved offer no indication of when this fact about $WKL_0$ was first noted. Thanks.