Stationary reflection and Prikry forcing, part 1
Seminar
Speaker
Yair Hayut (HUJI)
Date
03/03/2021 - 16:00 - 14:00Add to Calendar
2021-03-03 14:00:00
2021-03-03 16:00:00
Stationary reflection and Prikry forcing, part 1
In 1982, Magidor proved the consistency of stationary reflection at \aleph_{\omega+1}, relative to an \omega-sequence of supercompact cardinals.
Square based heuristics indicated that a much weaker large cardinal hypothesis is the correct strength.
In a sequence of results of various authors, Magidor's result was gradually improved to stationary reflection at all sets except one "bad" stationary set at \aleph_{\omega+1}, starting with a large cardinal property weaker than \kappa^+-supercompactness.
In a joint work with Unger, we managed to obtain the consistency of (full) stationary reflection, from what seems to be close to the optimal hypothesis.
In this talk I will present the main ideas behind the proof (which is the interplay between Prikry type forcings and iterated ultrapowers). This method shares some features with the Sigma-Prikry framework, where the main difference is its non-iterative nature.
In a joint work with Ben-Neria, we tackled the problem of combining the failure of SCH with stationary reflection, starting with a similar large cardinal hypothesis.
In order to do that, we used a similar analysis of the extender based Prikry forcing.
Link to video recording.
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אוניברסיטת בר-אילן - Department of Mathematics
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Abstract
In 1982, Magidor proved the consistency of stationary reflection at \aleph_{\omega+1}, relative to an \omega-sequence of supercompact cardinals.
Square based heuristics indicated that a much weaker large cardinal hypothesis is the correct strength.
In a sequence of results of various authors, Magidor's result was gradually improved to stationary reflection at all sets except one "bad" stationary set at \aleph_{\omega+1}, starting with a large cardinal property weaker than \kappa^+-supercompactness.
In a joint work with Unger, we managed to obtain the consistency of (full) stationary reflection, from what seems to be close to the optimal hypothesis.
In this talk I will present the main ideas behind the proof (which is the interplay between Prikry type forcings and iterated ultrapowers). This method shares some features with the Sigma-Prikry framework, where the main difference is its non-iterative nature.
In a joint work with Ben-Neria, we tackled the problem of combining the failure of SCH with stationary reflection, starting with a similar large cardinal hypothesis.
In order to do that, we used a similar analysis of the extender based Prikry forcing.
Link to video recording.
Last Updated Date : 07/03/2021
