Consistency statements in formal theories
Constructing Kripke models of certain fragments of Heyting's arithmetic.
Constructing ω-stable structures: Computing rank
This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.
Construction of an homology and a cohomology theory associated to a first order formula
Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9
Continuous Time Probability Logic
Core structures for theories
Corps C-minimaux, en l’honneur de François Lucas
La classe des constructibles de la géométrie algébrique est close par projection. La théorie des modèles exprime ce fait en disant que les corps algébriquement clos éliminent les quantificateurs dans le langage des anneaux. De façon analogue, les corps algébriquement clos non trivialement valués éliminent les quantificateurs dans le langage des anneaux enrichi de la relation dite de divisibilité . Cela implique en particulier la « -minimalité » : une partie définissable d’un corps algébriquement...
Corps équivalents à leur corps de séries
Cotorsion-free algebras as endomorphism algebras in - the discrete and topological cases
The discrete algebras over a commutative ring which can be realized as the full endomorphism algebra of a torsion-free -module have been investigated by Dugas and Göbel under the additional set-theoretic axiom of constructibility, . Many interesting results have been obtained for cotorsion-free algebras but the proofs involve rather elaborate calculations in linear algebra. Here these results are rederived in a more natural topological setting and substantial generalizations to topological...
Countable homogeneous coloured partial orders [Book]
Countable modules
Counting models of set theory
Let T denote a completion of ZF. We are interested in the number μ(T) of isomorphism types of countable well-founded models of T. Given any countable order type τ, we are also interested in the number μ(T,τ) of isomorphism types of countable models of T whose ordinals have order type τ. We prove: (1) Suppose ZFC has an uncountable well-founded model and . There is some completion T of ZF such that μ(T) = κ. (2) If α <ω₁ and μ(T,α) > ℵ₀, then . (3) If α < ω₁ and T ⊢ V ≠ OD, then . (4)...
Counting partial types in simple theories
We continue the work of Shelah and Casanovas on the cardinality of families of pairwise inconsistent types in simple theories. We prove that, in a simple theory, there are at most pairwise inconsistent types of size μ over a set of size λ. This bound improves the previous bounds and clarifies the role of κ(T). We also compute exactly the maximal cardinality of such families for countable, simple theories. The main tool is the fact that, in simple theories, the collection of nonforking extensions...
Counting rational points on a certain exponential-algebraic surface
We study the distribution of rational points on a certain exponential-algebraic surface and we prove, for this surface, a conjecture of A. J. Wilkie.
Counting sets
Craig Interpolation Theorem for Classical Propositional Logic with some Probability Operators
Craig's interpolation theorem, in computation theory
Si espongono alcuni risultati, provati dall’Autore negli articoli citati nella bibliografia, a proposito della complessità del teorema d’interpolazione di Craig: con ciò si intende la relazione tra la lunghezza (cioè il numero di simboli) della formula e la lunghezza di e , ove è un’implicazione valida, e è un interpolante, come esibito dal teorema di interpolazione stesso. Si intende altresì sottolineare la rilevanza dello studio della complessità dell’interpolazione per far luce su alcuni...
Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the...