Related papers: A constructive proof of Skolem theorem for constru…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a…
Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…
Intuitionistic first-order logic extended with a restricted form of Markov's principle is constructive and admits a Curry-Howard correspondence, as shown by Herbelin. We provide a simpler proof of that result and then we study…
The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure…
We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…
We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given a finite presentation of a (unitary) commutative ring…
The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…
In this paper we study an action of the absolute Galois group $\Gamma$ on bicolored plane trees induced by the action of $\Gamma$ on equivalence classes of conservative polynomials which are the simplest example of postcritically finite…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Let $\Gamma$ be a group acting on with finite stabilizers and finite fundamental domain on a building of type $\tilde A_2$. We prove that any non-trivial normal subgroup of $\Gamma$ is of finite index in $\Gamma$.
The Sylvester-Gallai Theorem, stated as a problem by J. J. Sylvester in 1893, asserts that for any finite, noncollinear set of points on a plane, there exists a line passing through exactly two points of the set. First, it is shown that for…
A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…
We show that the equational theory of the structure $\langle \omega^{\omega}: (x,y)\mapsto x+y, x\mapsto \omega x \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give…
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for several extensions of the ${\bf G3[mic]}$ sequent calculi…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Given a compact set K in the plane, which contains no triple of points forming a vertical and a horizontal segment, and a continuous real-valued map f on K, we give a construction of real-valued continuous maps of one variable g,h such that…