A note on cofinal extensions and segments
A note on noninterpretability in o-minimal structures
We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.
A partial order where all monotone maps are definable
It is consistent that there is a partial order (P,≤) of size such that every monotone function f:P → P is first order definable in (P,≤).
A saturation property on ideals
A weakening of the axiom of choice for the standard binary tree.
Absolutely saturated models
Almost direct products and saturation
An algebraic and logical approach to continuous images
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...
Banach-Mazur game played in partially ordered sets
Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.
Beaucoup de modèles à peu de frais
Boolean powers as algebras of continuous functions [Book]
Butler groups of infinite rank
Cardinalité, saturation et finitude
Čech-Stone remainders of spaces that look like
Chains in Ehrenfeucht Mostowski models
Compactness and homogeneity of saturated structures. I.
Compactness and homogeneity of saturated structures. II.
Compactness and homomorphisms of algebraic structures
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.