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Seminars "Proof Theory" and "Logic Online Seminar"
May 23, 2023 18:30, Moscow, Zoom
 


Non-linearities in the analytical hierarchy

J. P. Aguilera

Vienna, Gent, Hamburg
Video records:
MP4 203.2 Mb

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Video files:48



Abstract: It is commonly known that there exist true $\Pi^0_1$ sentences which are mutually independent over PA. The corresponding fact for $\Pi^1_1$ fails: for every pair of true $\Pi^1_1$ sentences $\phi,\psi$, one of them implies the other over ACA_0 + all true $\Sigma^1_1$ sentences. What about other classes, such as $\Pi^1_n$? We prove in ZFC + “there are infinitely many Woodin cardinals” that if $\Gamma$ = any of the classes $\Pi^1_{2n}$ or $\Sigma^1_{2n+1}$, then there are true $\Gamma$ sentences $\phi,\psi$ which are mutually independent over the theory ACA_0 + all true negations of $\Gamma$ sentences. This is joint work with F. Pakhomov.

Language: English
 
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