University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Computing beyond Constructibility: The Recognizability Stregth of Ordinal Time Machines

Computing beyond Constructibility: The Recognizability Stregth of Ordinal Time Machines

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact webseminars.

This talk has been canceled/deleted

Co-author: Philipp Schlicht (Universitt Bonn)

Transfinite machine models of computation provide an approach to an `effective mathematics of the uncountable’. However, their set-theoretical interest seems to be limited by the fact that even the strongest such model, Koepke’s Ordinal Turing Machines with parameters (pOTMs), can only compute constructible sets.

Recognizability is a more liberal notion than computability in that it only requires the machine to be able to identify a certain object when it is given to it as an input, not to produce that object.

By invoking notions from algorithmic randomness and considering recognizability rather than computability, we connect transfinite computability to large cardinals and forcing axioms incompatible with the axiom of constructibility on the one hand and inner models for large cardinals on the other. In particular, under appropriate large cardinal assumptions, a real number is heriditarily recognizable by a pOTM if and only if it is an element of the mouse for one Woodin cardinal. This is joint work with Philipp Schlicht.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

This talk is not included in any other list

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity