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Math 661 Topics in Mathematical Logic
MWF 1:15
Room 328
The topic will be quasi-finite axiomatisability and non finite axiomatisability. The main result in the area (which I doubt we will have time to prove) is by Hrushovski: A totally categorical theory is quasi-finitely axiomatisable, namely can be axiomatised by a single sentence together with the schema expressing the model is infinite.
We will definitely be proving the special case (due to Ziegler and Ahlbrandt) when T is almost strongly minimal, and the theorem (due to Cherlin-Harrington-Lachlan) that w-stable
w-categorical T is not finitely axiomatisable.
The main papers are:
1) w-categorical w-stable theories, Cherlin-Harrington-Lachlan, Annals of fPure &, Applied Logic 28 (1985)
2) Quasi-finitely axiomatisable totally categorical theories, Ahlbrandt and Ziegler, Annals of Pure & Applied Logic 30(1986)
3) Totally categorical structures, Hrushovski, preprint.
Anand Pillay
Harrington-Lachlan, Annals of Pure &#;ʄ~BCLMzuuu
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