### Sumários

##### Assessment with n mind changes

18 dezembro 2014, 09:00 • José Félix Costa

The finite difference hierarchy.

That a set of hipotheses is decidable with n mind changes starting with 0, given restriction K, iff, for all hypothesis h, C_h \cap K \in \sigma[K]^D_n.

Non-collapsing character of the finite difference hierarchy.

That the finite difference hierarchy \sigma^D_n is confined between \Sigma^B_1 and \Sigma^B_2 of the Borel hierarchy.

**** END OF COURSE 2014

##### Assessment in the limit

15 dezembro 2014, 13:00 • José Félix Costa

Borel hierarchy.

Non-collapsing character of Borel hierarchy over the Baire topological space. Collapse under restriction of the space to a countable number of observation trajectories.

That a set of hipotheses is verifiable in the limit given restriction K iff, for all hypothesis h, C_h \cap K \in \sigma[K]^B_2.

##### Assessment by time n and with certainty

11 dezembro 2014, 09:00 • José Félix Costa

Caracterization of the topological space of observations of the world (Baire space) for a science of verification, refutation and decidability of hypotheses by time n.

Caracterization of the topological space of observations of the world (Baire space) for a science of verification, refutation and decidability of hypotheses with certainty.

That Max(C,h) as optimal restriction of the possible observations of the world for the verification, refutation and decidability of hypotheses with certainty.

##### Baire topological space

4 dezembro 2014, 09:00 • José Félix Costa

Revision of topology: topological space, open and closed sets, limit points, interior and boundary of a set. Base of a topological space. Homeomorphisms.

Baire topological spaces. Fans and handles.

Caracterization of limit points in the Baire spaces. Relation between limit points and inductive scepticism.

Trees. n-uniform sets and uniformity.

Introduction to the application of the Baire spaces to several degrees of verification, refutation and decision: 'which topology of observations permits science to happen?'.

##### Vacillatory identification of sets II

1 dezembro 2014, 13:00 • José Félix Costa

Conclusion of vacillatory identification of sets.

**END OF CHAPTER 4 (CLASSES OF SCIENTISTS)**