We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the meaning of the new notion and its applications to call-by-name proof normalisation.
We give a simple intuitionistic completeness proof of Kripke semantics with constant domain for intuitionistic logic with implication and universal quantification. We use a cut-free intuitionistic sequent calculus as formal system and by combining soundness with completeness, we obtain an executable cut-elimination procedure. The proof, which has been… (More)
This paper presents GMeta: a generic framework for first-order representations of variable binding that provides once and for all many of the so-called infrastructure lemmas and definitions required in mechanizations of formal metatheory. The key idea is to employ datatype-generic programming (DGP) and modular programming techniques to deal with the… (More)
We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding which is universally defined for any function type, regardless of being impredica-tive. Direct and… (More)
— In an overview paper called State of the Art: Embedding Security in Vehicles, Wolf et al. give a general state-of-the-art overview of IT security in vehicles and describe core security technologies and relevant security mechanisms. In this paper we show that a formal analysis of many of the related properties is possible. This indicates that many expected… (More)
When mechanizing the metatheory of a programming language, one usually needs many lemmas proving structural properties of typing judgments, such as permutation and weakening. Such structural lemmas are sometimes unnecessary if we eliminate typing contexts by expanding typing judgments into their original hypothetical proofs. This technique of eliminating… (More)
The f-regressive Ramsey number R reg f (d, n) is the minimum N such that every colouring of the d-tuples of an N-element set mapping each x 1 ,. .. , x d to a colour ≤ f (x 1) contains a min-homogeneous set of size n, where a set is called min-homogeneous if every two d-tuples from this set that have the same smallest element get the same colour. If f is… (More)
This paper presents GMETA: a generic framework for first-order representations of variable binding that provides once and for all many of the so-called infrastructure lemmas and definitions required in mechanizations of formal metatheory. The framework employs datatype-generic programming and modular programming techniques to provide a universe representing… (More)
We give a combinatorial proof of a tight relationship between the Kanamori-McAloon principle and the Paris-Harrington theorem with a number-theoretic parameter function. We show that the provability of the parametrised version of the Kanamori-McAloon principle can exactly correspond to the relationship between Peano Arithmetic and the ordinal ε0 which… (More)