Presented By: Department of Mathematics
Logic
L_{omega_1,omega}-sentences with maximal models in two cardinalities
In this talk, we will present some examples on complete L_{omega_1,omega}-sentences with maximal models in (at least) two cardinalities.
Sample theorems:
Theorem: There is a complete L_{omega_1,omega}-sentence that characterizes aleph_2 and has maximal models in aleph_1 and aleph_2.
Theorem: Assume 2^{aleph_0}>aleph_n. Then there is a complete L_{omega_1,omega}-sentence with maximal models in cardinalities 2^{aleph_0}, 2^{\aleph_1},...,2^{aleph_n}.
The main construction behind these theorems is a refinement of a construction of J. Knight. This is recent work of J. Baldwin and the speaker. Speaker(s): Ioannis Souldatos (University of Detroit Mercy)
Sample theorems:
Theorem: There is a complete L_{omega_1,omega}-sentence that characterizes aleph_2 and has maximal models in aleph_1 and aleph_2.
Theorem: Assume 2^{aleph_0}>aleph_n. Then there is a complete L_{omega_1,omega}-sentence with maximal models in cardinalities 2^{aleph_0}, 2^{\aleph_1},...,2^{aleph_n}.
The main construction behind these theorems is a refinement of a construction of J. Knight. This is recent work of J. Baldwin and the speaker. Speaker(s): Ioannis Souldatos (University of Detroit Mercy)
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