Infinite coforcing in model theory

Infinite Time Computable Model Theory

We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time theory generalizes to the infinite time context, but several fundamental questions, including the infinite time computable analogue of the Completeness Theorem, t...

Infinite Permutation Groups in Enumeration and Model Theory

A permutation group G on a set Q has a natural action on Q for each natural number n. The group is called oligomorphic if it has only finitely many orbits on Q for all «GN. (The term means "few shapes". Typically our permutation groups are groups of automorphisms of structures of some kind; oligomorphy implies that the structure has only finitely many non-isomorphic w-element substructures for ...

Some Connections between Finite and Infinite Model Theory

Most of the work in model theory has, so far, considered infinite structures and the methods and results that have been worked out in this context can usually not be transferred to the study of finite structures in any obvious way; in addition, some basic results from infinite model theory fail within the context of finite models. The theory about finite structures has largely developed in conn...

Finite and Infinite Model Theory - A Historical Perspective

We describe the progress of model theory in the last half century from the standpoint of how finite model theory might develop.1

Some Connections between Finite and Infinite Model Theory