Michael Morley

• Cornell University

This chapter discusses a weak form of the Ehrenfeucht–Mostowski theorem, how to generate submodels, and extensions of the Ehrenfeucht–Mostowski theorem to non-elementary languages. The chapter presents an application of the Ehrenfeucht–Mostowski theorem to group theory and discusses the theories whose models contain relatively large homogenous sets...

A modelU is decidable if Th(U,a) a∈A is recursive. Various results about decidable models are discussed. A necessary and sufficient condition for there to be a decidable saturated model is given.

This chapter discusses countable models. For a fixed language the class is not an elementary class because there is no set of axioms that would guarantee that N would be isomorphic to the natural numbers. However, it is well known that there is a finite set of axioms whose models all have an initial segment isomorphic to the natural numbers with th...

Meeting of the Association for Symbolic Logic, Atlantic City, 1971 - Volume 36 Issue 4 - Michael O. Rabin, Michael Morley

A theory formulated in a countable predicate calculus can have at most nonisomorphic countable models. It has been conjected (e.g., in [4]) that if it has an uncountable number of such models then it has exactly such. Of course, this would follow immediately if one assumed the continuum hypothesis. In this paper we show that if a theory has more th...

This paper is an i exposition of some results that can be obtained by fairly simple methods, namely, the use of cardinality arguments and partition theorems. No results presented here are new but many of the proofs are. These may be of interest even to those already familiar with the results.

It is shown that, For each complete theoryT, the nomberh T(m) of homogeneous models ofT of powerm is a non-increasing function of uncountabel cardinalsm Moreover, ifh T(ℵ0)≦ℵ0, then the functionh T is also non-increasing ℵ0 to ℵ1.

Countable models of ℵ1-categorical theories are classified. It is shown that such a theory has only a countable number of nonisomorphic countable models.

This chapter focuses on omitting classes of elements. By a class of elements we mean a class defined by a set of formulas. It is fairly easy to show that there must be some cardinal, x, such that for any theory T and any class Σ the existence of a model of T of power K which omits Σ implies the existence of such models in each infinite power. The p...