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Seminars "Proof Theory" and "Logic Online Seminar"
November 11, 2019 18:30, Moscow, Steklov Mathematical Institute (8 Gubkina), room 313 + Zoom
 


Determined admissible sets

Juan Aguilera
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MP4 1,447.1 Mb

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Juan Aguilera



Abstract: We study the consistency strength of the axioms of determinacy for infinite games on the natural numbers and the real numbers, AD and AD_R respectively, in the context of Kripke-Platek set theory. We see that $\mathsf{KP} + \text{“}\mathbb{R}\text{ exists”} + \mathsf{AD}$ has strength similar to that of $\mathsf{ZF} + \mathsf{AD}$, while $\mathsf{KP} + \text{“}\mathbb{R}\text{ exists”} + \mathsf{AD}_{\mathbb{R}}$ is much weaker than $\mathsf{ZF} + \mathsf{AD}_{\mathbb{R}}$. The talk will be self-contained.

Language: English
 
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