Scattered sentences have few separable randomizations

Scattered Sentences Have Few Separable Randomizations

In the paper Randomizations of Scattered Sentences, Keisler showed that if Martin’s axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is “yes”. It follows that the absolute Vaught conjecture holds if and only if every Lω1ω-sentence with few separable randomization...

Separable Models of Randomizations

Every complete first order theory has a corresponding complete theory in continuous logic, called the randomization theory. It has two sorts, a sort for random elements of models of the first order theory, and a sort for events. In this paper we establish connections between properties of countable models of a first order theory and corresponding properties of separable models of the randomizat...

Do Sentences Have Tense?

A fact often not made explicit by syntacticians is that these labels need to be interpreted in semantics. The semantics of tenses has been formulated as a theory of temporal reference since the seminal work of Reichenbach (1947). Subsequently this theory has been integrated into a theory of context change, which widens the domain of tense semantics from the sentence to discourse (Kamp. 1979, Ka...

Weak NP’s in HAVE Sentences

Definable closure in randomizations

The randomization of a complete rst order theory T is the complete continuous theory T with two sorts, a sort for random elements of models of T , and a sort for events in an underlying probability space. We give necessary and su cient conditions for an element to be de nable over a set of parameters in a model of T.