Morley's problem

Morley's problem is a conjecture (first proposed by Frank Morley) in mathematical logic that if T is a countable first order theory and for an uncountable cardinal lambda, f_T(lambda) denotes the number of nonisomorphic models of cardinality lambda, then f_T(lambda) is nondecreasing in lambda. This was proved by Saharon Shelah. For this, he proved a very deep dichotomy theorem.

Related Topics:
Conjecture - Frank Morley - Mathematical logic - Countable - First order theory - Uncountable - Cardinal - Nonisomorphic - Models - Cardinality - Nondecreasing - Saharon Shelah

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Saharon Shelah, "Classification theory and the number of nonisomorphic

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models.", volume 92 of Studies in Logic and the Foundations of Math-

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ematics North Holland, 1990?-->

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