Mathematics Problem Archive

Classify reasonable increasing functions on the Turing degrees; Martin's conjecture predicts that they are essentially iterates of the Turing jump....

Over $\mathsf{RCA}_0$, is $\mathsf{IPT}^2_2$ equivalent to $\mathsf{RT}^2_2$?...

Over $\mathsf{RCA}_0$, is Hindman's theorem equivalent to $\mathsf{ACA}^+_0$, equivalent to $\mathsf{ACA}_0$, or strictly between them?...

Determine the reverse-mathematical strength of the dual Ramsey theorem $\mathsf{DRT}^k$....

Determine the reverse-mathematical strength of the Carlson–Simpson infinite-variable-word lemma $\mathsf{CS}$....

Over $\mathsf{RCA}_0$, does the Lebesgue differentiation theorem imply $\mathsf{WWKL}_0$?...

Over $\mathsf{RCA}_0$, is the Auslander–Ellis theorem equivalent to $\mathsf{ACA}_0$?...

Over $\mathsf{RCA}_0$, is $\mathsf{EXT}(\omega^*)$ — the assertion that every well-founded partial order has a well-ordered linearization — equivalent...

Over $\mathsf{RCA}_0$, is Fraïssé's conjecture for countable linear orders equivalent to $\mathsf{ATR}_0$?...

Is there a subsystem weaker than $\mathsf{ATR}_0$ that proves that the three-element antichain is a better-quasi-order?...

Over $\mathsf{RCA}^*_0$, is Ramsey's theorem for triples equivalent to $\mathsf{ACA}_0$, as it is over $\mathsf{RCA}_0$?...