38 citations · 45 across the 7 of their papers we have counts for
8 papers
Continuous Craig Interpolation
H. Jerome Keisler
We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.
Using Ultrapowers to Compare Continuous Structures
H. Jerome Keisler
In 1967 the author introduced a pre-ordering of all first order complete theories where T is lower than U if it is easier for an ultrapower of a model of T than an ultrapower of a…
Model Theory for Real-valued Structures
H. Jerome Keisler
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly co…
Continuous Sentences Preserved Under Reduced Products
Isaac Goldbring, H. Jerome Keisler
Answering a question of Cifú Lopes, we give a syntactic characterization of those continuous sentences that are preserved under reduced products of metric structures. In fact, we s…
Scattered Sentences have Few Separable Randomizations
Uri Andrews, Isaac Goldbring, Sherwood Hachtman +2
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…
Algebraic Independence Relations in Randomizations
Uri Andrews, Isaac Goldbring, H. Jerome Keisler
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations of complete first order theories…
Independence relations in randomizations
Uri Andrews, Isaac Goldbring, H. Jerome Keisler
The randomization of a complete first order theory is the complete continuous theory with two sorts, a sort for random elements of models of , and a sort for events in…
Randomizations of models as metric structures
Itaï Ben Yaacov, H. Jerome Keisler
The notion of a randomization of a first order structure was introduced by Keisler in the paper Randomizing a Model, Advances in Math. 1999. The idea was to form a new structure wh…