07/05/ 2012 - 14h00
Abstract: The story of modern
metamathematics started in 1976 with the emergence of (the early versions of)
the Paris-Harrington Principle and Friedman's successful initiation of the
Reverse Mathematics Programme. Since that time, three generations of dramatical
and conflicting metamathematical ideas emerged, including the crisis of 1985 -
1989, when most researchers left the field in pessimism or dispair.
In the first half of the talk I will sketch the history of metamathematics and a kaleidoscope of old (20th century, now outdated) ideas, and the new promising ideas, intuitions, programmes and methods, and motivations behind them, including: Harvey Friedman's machinery and results and Andreas Weiermann's programme of finding threshold versions of unprovability results.
In the second half of the talk, I will speak about the new results (and motivations behind them) done by me and my students and collaborators (mostly Michiel De Smet and Zachiri McKenzie), and the bigger programmes that guide these investigations: the search for Arithmetical Splitting, the study of the Atlas of All Possibilities, the search for the 'true reasons´ for unprovability, the notion of 'wrapping´ axiom schemes, and some Infinite-Dimensional Ramsey Theory.
I will also mention how metamathematical developments since 1976 affected philosophy of mathematics.
The talk will be very simple
and accessible to everyone interested in Unprovability.
COPPE
Centro de Tecnologia
Bloco F sala F110- UFRJ
Centro de Tecnologia
Bloco F sala F110- UFRJ
