Related papers: Conservation theorems for the Cohesiveness Princip…

We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result shows that fin-COH entails $I\Sigma_1^0$ over the weaker base…

Let $\mathsf{TT}^1$ be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let $\mathsf{RT}^2_2$ and $\mathsf{WKL}_0$ denote respectively the principles of…

We prove conservativity results for weak K\H{o}nig's lemma that extend the celebrated result of Harrington (for $\Pi^1_1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form…

In this article, we prove that Ramsey's theorem for pairs and two colors is $\Pi^1_1$-conservative over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \mathsf{WF}(\epsilon_0)$ and over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \bigcup_n…

We prove that if $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are countable models of the theory $\mathrm{WKL}^*_0$ such that $\mathrm{I}\Sigma_1(A)$ fails for some $A \in \mathcal{X} \cap \mathcal{Y}$, then $(M,\mathcal{X})$ and…

An open question in reverse mathematics is whether the cohesive principle, $\COH$, is implied by the stable form of Ramsey's theorem for pairs, $\SRT^2_2$, in $\omega$-models of $\RCA$. One typical way of establishing this implication would…

In this paper, we show that $\mathrm{RT}^{2}+\mathsf{WKL}_0$ is a $\Pi^{1}_{1}$-conservative extension of $\mathrm{B}\Sigma^0_3$.

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between…

The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstra{\ss} principle (BW) and a weak variant of it. We show that BW is instance-wise equivalent to the weak K\"onig's lemma for…

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf{PA}$ and intuitionistic arithmetic $\mathsf{HA}$. Using a generalized negative translation, we first…

A left-variable word over an alphabet~$A$ is a word over~$A \cup \{\star\}$ whose first letter is the distinguished symbol~$\star$ standing for a placeholder. The Ordered Variable Word theorem ($\mathsf{OVW}$), also known as…

We show that over the weak base theory $\mathrm{RCA}_0^*$, cohesive Ramsey's theorem for pairs $\mathrm{CRT}^2_2$ implies exponential closure of the definable cut $\mathrm{I}^0_1$, which is the intersection of all $\Sigma^0_1$-definable…

Kruskal's theorem famously states that finite trees (ordered using an infima-preserving embeddability relation) form a well partial order. Freund, Rathjen, and Weiermann extended this result to general recursive data types with their…

In this article, we prove that Ramsey's theorem for pairs and two colors is a $\forall \Pi^0_4$ conservative extension of $\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2$, where a $\forall \Pi^0_4$ formula consists of a universal quantifier over…

In this paper the lightface $\Pi^{1}_{1}$-Comprehension axiom is shown to be proof-theoretically strong even over $\mbox{RCA}_{0}^{*}$, and we calibrate the proof-theoretic ordinals of weak fragments of the theory $\mbox{ID}_{1}$ of…

The paper is devoted to a reverse-mathematical study of some well-known consequences of Ramsey's theorem for pairs, focused on the chain-antichain principle $\mathsf{CAC}$, the ascending-descending sequence principle $\mathsf{ADS}$, and the…

We provide a general preservation theorem for preserving selective independent families along countable support iterations. The theorem gives a general framework for a number of results in the literature concerning models in which the…

We prove that any proof of a $\forall \Sigma^0_2$ sentence in the theory $\mathrm{WKL}_0 + \mathrm{RT}^2_2$ can be translated into a proof in $\mathrm{RCA}_0$ at the cost of a polynomial increase in size. In fact, the proof in…

Let $\mathsf{TT}^2_k$ denote the combinatorial principle stating that every $k$-coloring of pairs of compatible nodes in the full binary tree has a homogeneous solution, i.e. an isomorphic subtree in which all pairs of compatible nodes have…

We analyze Ekeland's variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to $\Pi^1_1$-${\sf CA}_0$, a strong theory of second-order arithmetic, while natural…