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Glivenkos theorem states that a formula is derivable in classical propositional logic $mathrm{CL}$ iff under the double negation it is derivable in intuitionistic propositional logic $mathrm{IL}$: $mathrm{CL}vdashvarphi$ iff $mathrm{IL}vdash eg egvarphi$. Its analog for the modal logics $mathrm{S5}$ and $mathrm{S4}$ states that $mathrm{S5}vdash varphi$ iff $mathrm{S4} vdash eg Box eg Box varphi$. In Kripke semantics, $mathrm{IL}$ is the logic of partial orders, and $mathrm{CL}$ is the logic of partial orders of height 1. Likewise, $mathrm{S4}$ is the logic of preorders, and $mathrm{S5}$ is the logic of equivalence relations, which are preorders of height 1. In this paper we generalize Glivenkos translation for logics of arbitrary finite height.
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $mc{NP}$-complete; for $L$ of height at least $3$, equ
The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the classical Omitti
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 $mathrm{RCA}_0$ can be found
Inspired by Ramseys theorem for pairs, Rival and Sands proved what we refer to as an inside/outside Ramsey theorem: every infinite graph $G$ contains an infinite subset $H$ such that every vertex of $G$ is adjacent to precisely none, one, or infinite
We analyze the strength of Hellys selection theorem HST, which is the most important compactness theorem on the space of functions of bounded variation. For this we utilize a new representation of this space intermediate between $L_1$ and the Sobolev