Related papers: The Logic of Correct Models
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the…
Let \phi be a first order formula and M be a countable model. \phi^M denotes the set of all assignments that satisfy \phi in M. Let M, N be countable models. A formula \phi distinguishes these models if |\phi^M|\neq |\phi^N|. We show that…
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
We consider well-known provability logic GLP. We prove that the GLP-provability problem for variable-free polymodal formulas is PSPACE-complete. For a number n, let L^n_0 denote the class of all polymodal variable-free formulas without…
We define a infinitary labelled sequent calculus for PDL, G3PDL^{\infty}. A finitarily representable cyclic system, G3PDL^{\omega}, is then given. We show that both are sound and complete with respect to standard models of PDL and, further,…
Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and L\"owe studied the modal logical aspects of set theoretic multiverse and proved that the modal…
We show that the category of motivic spaces with transfers along finite flat morphisms, over a perfect field, satisfies all the properties we have come to expect of good categories of motives. In particular we establish the analog of…
We introduce the $\Sigma_1$-definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, (i) the sequence is $\Sigma_1$-definable…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction of GLP to its important fragment called J syntactically.
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
In this short note we give an alternative proof of Glivenko's Theorem, stating that a formula $\phi$ is provable in classical propositional logic if and only if $\neg\neg\phi$ is provable in intuitionistic propositional logic. We work in…
We prove preservation theorems for $\mathcal{L}_{\omega_1, G}$, the countable fragment of Vaught's closed game logic. These are direct generalizations of the theorems of \L{}o\'s-Tarski (resp. Lyndon) on sentences of $\mathcal{L}_{\omega_1,…
In 1997 Timothy J. Surendonk proved via algebraic semantics that all modal logics without iterative axioms are canonical and so strongly complete. In this paper, we continue the work done by Surendonk in this field. We use neighborhood…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
A proof of G\"odel's incompleteness theorem is given. With this new proof a transfinite extension of G\"odel's theorem is considered. It is shown that if one assumes the set theory ZFC on the meta level as well as on the object level, a…