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On semialgebraic points of definable sets

Artur Piękosz (1998)

Banach Center Publications

We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.

On sets with rank one in simple homogeneous structures

Ove Ahlman, Vera Koponen (2015)

Fundamenta Mathematicae

We study definable sets D of SU-rank 1 in ℳ e q , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in ℳ e q , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...

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...

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

Relations between Shy Sets and Sets of ν p -Measure Zero in Solovay’s Model

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

An example of a non-zero non-atomic translation-invariant Borel measure ν p on the Banach space ℓ p ( 1 ≤ p ≤ ∞ ) is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition " ν p -almost every element of ℓ p has a property P" implies that “almost every” element of ℓ p (in the sense of [4]) has the property P. It is also shown that the converse is not valid.

Rigid ℵ ε -saturated models of superstable theories

Ziv Shami, Saharon Shelah (1999)

Fundamenta Mathematicae

In a countable superstable NDOP theory, the existence of a rigid ﬡ ε -saturated model implies the existence of 2 λ rigid ﬡ ε -saturated models of power λ for every λ > 2 ﬡ 0 .

Currently displaying 41 – 60 of 76