University of Connecticut

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Connecticut Logic Seminar
On $$\Sigma$$--preorderings in $$\text{HF}(\mathbb{R})$$
Andrey Morozov (Sobolev Institute of Mathematics and Novosibirsk State University)

Monday, February 24, 2020
4:45pm – 6:00pm

Exley 618, Wesleyan University

We prove that $$\omega_1$$ cannot be embedded into any preordering $$\Sigma$$-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF($$\mathbb{R}$$). As corollaries, we obtain characterizations of $$\Sigma$$-presentable ordinals and Godel constructive sets of kind $$L_\alpha$$. It also follows that there are no $$\Sigma$$-presentations for structures of $$T$$-, $$m$$-, $$1$$-, and $$tt$$-degrees over HF($$\mathbb{R}$$).


Reed Solomon,

Connecticut Logic Seminar (primary), College of Liberal Arts and Sciences, UConn Master Calendar

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