相关论文: An isomorphism theorem for models of Weak K\"onig'…

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…

We prove that the Cohesiveness Principle (COH) is $\Pi^1_1$ conservative over $RCA_0 + I\Sigma^0_n$ and over $RCA_0 + B\Sigma^0_n$ for all $n \geq 2$ by recursion-theoretic means. We first characterize COH over $RCA_0 + B\Sigma^0_2$ as a…

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 that if the linear-time and polynomial-time hierarchies coincide, then every model of $\Pi_1(\mathbb{N}) + \neg \Omega_1$ has a proper end-extension to a model of $\Pi_1(\mathbb{N})$, and so $\Pi_1(\mathbb{N}) + \neg \Omega_1…

We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigma_n and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi_2 complete. Along the way, we…

In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…

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 show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…

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…

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…

We study the first-order consequences of Ramsey's Theorem for $k$-colourings of $n$-tuples, for fixed $n, k \ge 2$, over the relatively weak second-order arithmetic theory $\mathrm{RCA}^*_0$. Using the Chong-Mourad coding lemma, we show…

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize…

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…

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…

A set of integers $A$ is computably encodable if every infinite set of integers has an infinite subset computing $A$. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this paper, we extend this…

The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…

The proofs of K. Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we formulate and prove a Weak Coherence Theorem without using Weierstrass' Preparation Theorem, but only with power series expansions:…

(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…

We define weak units in a semi-monoidal 2-category $\CC$ as cancellable pseudo-idempotents: they are pairs $(I,\alpha)$ where $I$ is an object such that tensoring with $I$ from either side constitutes a biequivalence of $\CC$, and $\alpha:…

We derive a new sufficient condition for the existence of {\omega}-categorical universal structures in classes of relational structures with constraints, augmenting results by Cherlin, Shelah, Chi, and Hubi\v{c}ka and Ne\v{s}et\v{r}il.…