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SUMMARY:Anton Freund (Universit&auml\;t W&uuml\;rzburg)
DTSTART:20250925T180000Z
DTEND:20250925T190000Z
DTSTAMP:20260423T035918Z
UID:OLS/186
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/186/">We
 ll-ordering principles and the reverse mathematics zoo</a>\nby Anton Freun
 d (Universit&auml\;t W&uuml\;rzburg) as part of Online logic seminar\n\n\n
 Abstract\nOver the moderately strong base theory ACA$_0$ from reverse math
 ematics\, any $\\Pi^1_2$-statement corresponds to a transformations of wel
 l-orders (i.e.\, to a dilator). We will show that\, in contrast\, there is
  a dichotomy over the weaker base theory RCA$_0$. Here\, transformations o
 f well-orders are either weak or have a certain minimal strength. It follo
 ws that $\\Pi^1_2$-statements in a certain gap cannot correspond to a tran
 sformation of well-orders. Ramsey's theorem for pairs is a particularly pr
 ominent $\\Pi^1_2$-statement in this gap. The talk is based on <a href="ht
 tps://doi.org/10.1142/S0219061325500102">https://doi.org/10.1142/S02190613
 25500102</a>. It is directed at a general logical audience.\n
LOCATION:https://researchseminars.org/talk/OLS/186/
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