An unfinitizability proof by means of restricted reduced power
Analytic cell decomposition and analytic motivic integration
Analytic Tableaux and Interpolation
Anelli regolari separabilmente chiusi
Another approach to infinite forcing
Anzahlquantoren in der Prädikatenlogik
Application of a Tauberian theorem to finite model theory.
Applications logiques en théorie des anneaux et des modules
Applications of Model Theory to Representations of Finite-Dimensional Algebras.
Applications of ultrapowers and Lipschitz classification of Banach spaces
Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces
Approximating the standard model of analysis
Approximation Properties and Existential Completeness for Ring Morphisms.
Approximation theory of uniqueness conditions by existence conditions
Arithmetization of the field of reals with exponentiation extended abstract
(1) Shepherdson proved that a discrete unitary commutative semi-ring A+ satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with exponentiation; for three values of T we provide a theory in the language of rings plus exponentiation such that the ...
Around Podewski's conjecture
A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of...
Around stable forking
We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.
Atomic compactness and elementary equivalence
Atomic compactness for reflexive graphs
A first order structure with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their...
Atomic compactness in - categorical Horn theories