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Comparing the Complexity of Unstable Theories
Published on May 20, 20114454 Views
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Chapter list
Comparing the complexity of unstable theories00:00
Cantor's proof (1)00:11
Cantor's proof (2)01:12
Model theory as the "geography of mathematics"03:52
A framework for comparing countable theories (1)07:45
A framework for comparing countable theories (2)09:49
Keisler's order: formal version10:43
Results on Keisler's order, 1967-197813:09
The unstable case: Localization (1)17:00
The unstable case: Localization (2)17:26
Formula complexity via characteristic sequence18:01
The exploration begins, [3], [4]20:23
Shelah's classic "dichotomy" for unstable theories21:29
Rigidity/randomness22:04
In our context, within the independent theories...22:26
the random graph is minimum22:38
and since strict order is maximum22:59
the random graph is minimum among all unstable theories23:10
Shelah: a \dichotomy" above simple theories23:18
Two kinds of tree property23:43
The "independent side" of the dichotomy24:00
Theorem, Malliaris [5]24:03
Remark24:15
Canonicity of these examples (1)24:52
Canonicity of these examples (2)25:32
Canonicity of these examples (3)26:52
Graph theory: a new language suggests new structure27:16
Theorem (Malliaris 2010 [4])28:54
By way of conclusion31:29
References32:44