Online research in philosophy

We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ does not (...) fork over $\emptyset$ , precisely as in stable groups, answering positively an earlier problem posed by the first two authors. (shrink)

We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius r < 1 contained in the valuation ring and the set of balls of a given multiplicative radius r < 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and only if its (...) algebraic closure is stably embedded. (shrink)

Orthogonality between two stably embedded definable sets is preserved under the addition of constants.

Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.

Ne estas prima orda formulo, kiu definas la Zariskijajn slositojn inter la konstruitoj, malpli ke la konektojn inter la slositoj.

Finitely axiomatizable ℵ 1 categorical theories are locally modular.

A stable theory is finitely based if every set of indiscernibles is based on a finite subset. This is a common generalization of superstability and 1-basedness. We show that if such theories have more than one model they must have infinitely many, and prove some other conjectures.

Kueker's conjecture is proved for stable theories, for theories that interpret a linear ordering, and for theories with Skolem functions. The proof of the stable case involves certain results on coordinatization that are of independent interest.