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SUMMARY:Jorge Cruz Chapital (University of Trononto)
DTSTART:20260212T190000Z
DTEND:20260212T200000Z
DTSTAMP:20260423T021240Z
UID:OLS/203
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/203/">Co
 nstruction schemes: Finitizations of guessing principles and their paramet
 rized forcing axioms.</a>\nby Jorge Cruz Chapital (University of Trononto)
  as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we survey r
 ecent developments in the theory of capturing schemes introduced by Todorc
 evic. We present the capturing axioms CAρ​\, CAΔ​\, and CA\, which m
 ay be viewed as finite-dimensional analogues of the classical guessing pri
 nciples Club\, CH\, and Diamond\, respectively. We show that many conseque
 nces traditionally derived from these guessing principles already follow f
 rom the capturing axioms\, often with significantly simpler proofs. Finall
 y\, we introduce parametrized forcing axioms naturally associated with the
  capturing principles and demonstrate how they can be used to establish th
 e independence of a strong statement about gaps over ω\, a problem that c
 annot be settled using either traditional guessing principles or standard 
 forcing axioms.\n
LOCATION:https://researchseminars.org/talk/OLS/203/
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