Mathematics Problem Archive

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

For any finite sets $X$ and $Y$ of published mathematical theorems expressible in second-order arithmetic, is either $\mathsf{RCA}_0+X$ interpretable ...

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 $\mathsf{CS}$....

Are the following statements equivalent to $\Pi^1_1\text{-}\mathsf{CA}_0$? (i) If countable torsion abelian groups $G,H$ satisfy $G\oplus G\cong H\opl...

Determine the reverse-mathematical strength of Alexandroff's one-point compactification theorem for countably based MF spaces....

Determine the reverse-mathematical strength of the assertion that a proper MF space is metrizable if and only if it is regular....

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 $\mathsf{RCA}_0$, does the Furstenberg–Zimmer structure theorem imply $\Pi^1_1\text{-}\mathsf{CA}_0$?...

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 $\mathsf{ATR}_0$?...

For an ordinal $\alpha$, determine the length (maximal order type) of the well-quasi-order $L_\alpha$ of countable linear orders of Hausdorff rank bel...

Determine the reverse-mathematical strengths of Laver's labeled-linear-order theorem $\mathsf{LAV}$ and the Nash–Williams bqo transfinite-sequence the...

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

Is weak-$L_{\omega_1,\omega}$-$\mathsf{CA}$ equivalent to weak-$\Sigma^1_1$-$\mathsf{AC}_0$?...

Is the open mapping theorem for separable Banach spaces provable in $\mathsf{RCA}_0$, or at least in $\mathsf{WKL}_0$?...

Determine the exact reverse-mathematical strength of the Krein–Šmulian theorem for separable Banach spaces....

Is Szemerédi's theorem provable in $\mathsf{ACA}_0$? More generally, determine its reverse-mathematical strength....

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