Showing papers in "Annals of Pure and Applied Logic in 1998"

TL;DR: Structures equipped with generic predicates and/or automorphisms are studied, and it is shown that in many cases they obtain simple theories.

TL;DR: It is proved that every monadic second-order property of the unfolding of a transition system is a monadicsecond-orderproperty of the system itself.

TL;DR: This work considers Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank, and relates the descriptive complexity of the equivalence relation to the nature of its complete invariants.

TL;DR: It is proved that any computable partially ordered set is isomorphic to the spectrum of an intrinsically c.e. relation on a computable structure, and the isomorphism can be constructed in such a way that the image of the minimum element of the partially ordering set is computable.

TL;DR: These proofs, together with an embedding of the type theory in a set theoretical system as carried out in Setter (1993), show that the proof theoretical strength of Martin-Lof's type theory with W-type and one universe is strong.

TL;DR: It is shown that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density, and every finite dimensional (or locally finite dimensional) rich algebra of logic is representable.

TL;DR: The axioms of CZF are extended and it is shown that the resulting theory, when augmented by the tertium non-datur, is equivalent to ZF plus the assertion that there are inaccessibles of all transfinite orders.

TL;DR: The attic is gathered to gather miscellaneous results in proof theory from the attic, including an equivalence between transfinite induction rule and iterated reflection schema over IΣn, and proof theoretic strengths of classical fixed points theories.

TL;DR: It is shown that not every (infinitary) first-order theory has a classifying topos in this sense, but those which do by an appropriate ‘smallness condition’ are characterized by the Heyting-valued completeness theorem for infinitary first- order logic.

TL;DR: A Π01 class is an effectively closed set of reals determined by cardinality, measure and category as well as by the complexity of the members of a class P.

TL;DR: The Gap Forcing Theorem (GCH) of as discussed by the authors implies that after any reverse Easton iteration of closed forcing, such as the Laver preparation, every supercompactness measure on a super-compact cardinal extends a measure from the ground model.

TL;DR: It is shown that there exists subsets A and B of the real line which are recursively constructible such that A has a nonrecursive Hausdorff dimension and B has a recursive Hausdorf dimension but has a finite, nonrecursion-based measure.

TL;DR: This work defines Dg A (R) to be the set of Turing degrees of the images f(R) under all isomorphisms f from A to computable models and investigates conditions on A and R which are sufficient and necessary to contain every Turing degree.

TL;DR: A uniform approach for proving several meta-theorems relating properties of λ-terms and their typability in the systems D and D Ω and characterize the terms that have weak head-normal forms, which appears to be new.

TL;DR: This work considers the computably enumerable sets under the relation of Q-reducibility, and uses coding methods to show that the elementary theory of 〈RQ, ⩽Q〉 is undecidable.

TL;DR: Cette notion constructive permet une relecture de la theorie d'Artin-Schreier, avec la modification capitale that le resultat final est alors etabli de maniere constructive.

TL;DR: It is proved that if M is an inner model of set theory and the set of reals in M is analytic then either all reals are in $M$ or else $\aleph _1^M$ is countable.

TL;DR: The numerical strength of fragments of arithmetical comprehension, choice and general uniform boundedness is studied systematically and provably recursive function(al)s of type ⩽2 of the extensions of T n ω are characterized based on these fragments.

TL;DR: A first order axiom set is described which yields the classical first order Euclidean geometry of Tarski when used with classical logic, and yields an intuitionistic (or constructive) Euclideans geometry when using with intuitionistic logic.

TL;DR: It turns out that the notion of randomness defines, in a natural way, an algebra that is computably enumerable and finitely generated.

TL;DR: A point-free approach to the study of topological spaces and functions on them is developed, platforms for both are established and some findings on recursive points are presented.

TL;DR: Two applications of the main Theorem to set theory are presented and a theorem of Magidor's on covering between models of ZFC is proved.

TL;DR: The nonstandard stroboscopy method is extended to an elementary, yet general class of partial difference/differential equations, both of first and second order, and creates intermediary objects: partial difference equations with S-continuous solutions, which have both discrete and continuous properties.

TL;DR: It is proved that the boundedness theorem of generalized recursion theory can be derived from the ω-completeness theorem for number theory, and a proof of the boundeds theorem which does not refer to the analytical hierarchy theorem.

TL;DR: A new kind of genericity is defined, dynamic genericity, and it is proved that it is stronger than pb-genericity, to examine the relation between genericity and array noncomputability and derive some structural information about the Δ20 degrees.

TL;DR: New ∄-definable properties relating the∄-structure of A to deg( A), which answer some open questions are introduced, and a related property NL ( A) is presented which has a slower flow but fast enough to guarantee that A is not low, even though A may possess virtually all other related lowness properties and A may simultaneously be promptly simple.

TL;DR: Godel's interpretation of T is extended to theories Pn of “predicative” functionals, which are defined using Martin-Lof's universes of transfinite types, so that each ⌢ID n is interpreted in the corresponding Pn.

TL;DR: This work approaches the subject of o-minimality from the point of view of tame systems, following the work of Charbonnel and Wilkie, and is able to obtain the following generalisation of a recent result of Gabrielov.

TL;DR: The method to build notation systems for infinite sequent-style derivations, analogous to well-known systems of notation for ordinals, is extended to the more general setting of infinite (typed) terms in order to make it applicable in other proof-theoretic contexts as well as in recursion theory.

TL;DR: The main result shows that any computable theory T of intuitionistic predicate logic has a Kripke model with decidable forcing such that for any sentence φ, φ is forced in the model if and only ifπ is intuitionistically deducible from T.