University Seminar: Logic Across Disciplines- On Sigma preorderings in HF(R)

Title: On Sigma preorderings in HF(R)
Speaker: Andrei Morozov, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Date and Time: Thursday, February 20, 3:45PM-5:00PM
Place: Phillips Hall (801 22nd Street), Room 736

Abstract:  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(R).
As corollaries, we obtain characterizations of Sigma-presentable ordinals and Goedel constructive sets of kind L_alpha. It also follows that there are no Sigma-presentations for structures of Turing degrees and strong degrees, over HF(R).