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P-NDOP and P-decompositions of ℵ ϵ -saturated models of superstable theories

Saharon Shelah, Michael C. Laskowski (2015)

Fundamenta Mathematicae

Given a complete, superstable theory, we distinguish a class P of regular types, typically closed under automorphisms of ℭ and non-orthogonality. We define the notion of P-NDOP, which is a weakening of NDOP. For superstable theories with P-NDOP, we prove the existence of P-decompositions and derive an analog of the first author's result in Israel J. Math. 140 (2004). In this context, we also find a sufficient condition on P-decompositions that implies non-isomorphic models. For this, we investigate...

Poincaré - Verdier duality in o-minimal structures

Mário J. Edmundo, Luca Prelli (2010)

Annales de l’institut Fourier

Here we prove a Poincaré - Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.

Potential isomorphism and semi-proper trees

Alex Hellsten, Tapani Hyttinen, Saharon Shelah (2002)

Fundamenta Mathematicae

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees. ...

Preliminaries to Classical First Order Model Theory

Marco Caminati (2011)

Formalized Mathematics

First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretations and sequent derivation rules, respectively, are confined to separate articles, to mark out the hierarchy...

Prescribing endomorphism algebras of ℵ n -free modules

Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)

Journal of the European Mathematical Society

It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...

Properties of extensions of algebraically maximal fields.

G. Leloup (2003)

Collectanea Mathematica

We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.

Currently displaying 681 – 700 of 1342