逻辑

We study the effective versions of several notions related to incompleteness, undecidability and inseparability along the lines of Pour-El's insights. Firstly, we strengthen Pour-El's theorem on the equivalence between effective essential…

In this paper, we study the employment of $\Sigma_1$-sentences with certificates, i.e., $\Sigma_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some…

We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…

We define and study the class of inner ultrahomogeneous groups, which includes Hall's universal group and the universal locally recursively presentable group. We provide simple criteria for ample generic automorphisms, straight maximality,…

We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.

We prove that for every colouring of pairs of reals with finitely-many colours, there is a set homeomorphic to the rationals which takes no more than two colours. This was conjectured by Galvin in 1970, and a colouring of Sierpi{\'n}ski…

Fix $n=1,2,3,\dots$ or $n=\omega$. We prove a dichotomy for Borel homomorphisms from the $n$-th Friedman-Stanley jump $=^{+n}$ to an equivalence relation $E$ which is classifiable by countable structures: if there is no reduction from…

The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…

In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant…

We present recent results on the model companions of set theory, placing them in the context of the current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the…

Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…

The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between ultrafilter extensions and ultrapowers. We show that certain…

We develop the non-normal variations of two classical Prikry-type forcings; namely, Magidor and Radin forcings. We generalize the fact that the non-normal Prikry forcing is a projection of the extender-based to a coordinate of the extender…

In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…

We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…

We show that, in general, there is no degree corresponding to the composition of two problems in the computable reducibility lattice.

We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra…

It is an open question whether compositional truth with the principle of propositional soundness ,,all arithmetical sentences which are propositional tautologies are true'' is conservative over its arithmetical base theory. In this article,…

The famous theorem of Higman states that for any well-quasi-order (wqo) $Q$ the embeddability order on finite sequences over $Q$ is also wqo. In his celebrated 1965 paper, Nash-Williams established that the same conclusion holds even for…

An embedding of arbitrary Heyting algebra H into a reduct from the variety of Kuznetsov-Muravitsky algebras is constructed. An algebraic proof is given that this reduct belongs to the variety of Heyting algebras generated by H.