Applications logiques en théorie des anneaux et des modules
Applications of Model Theory to Representations of Finite-Dimensional Algebras.
Approximation Properties and Existential Completeness for Ring Morphisms.
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...
Automorphisms of Bounded Abelian Groups.
Banach spaces and large cardinals
Boolean powers as algebras of continuous functions [Book]
Boolean spectra and model completions
Boolean valued rings
Bounded products in the theory of valued fields.
Cancellation of Abelian groups of finite rank modulo elementary equivalence.
Categorical models and quasigroup homotopies.
C'est beau et chaud
Compactness and homogeneity of saturated structures. II.
Complete and model-complete theories of monadic algebras
Computing the Galois group of a linear differential equation
Concerning basic notions of the measurement theory
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.
Corps équivalents à leur corps de séries