Sumários
Assessment in the limit and gradual assessment
12 dezembro 2017, 15:00 • José Félix Costa
Borel hierarchy.
Non-collapsing character of Borel hierarchy over the Baire topological space.
That a set of hipotheses is C-verifiable, C-refutable, C-decidable in the limit given K iff, for all hypothesis h, C_h \cap K is in \Sigma[K]^B_2, \Pi[K]^B_2 \Delta[K]^B_2, respectively.
That a set of hipotheses is C-verifiable gradually, C-refutable gradually, C-decidable gradually given K iff, for all hypothesis h, C_h \cap K is in \Pi[K]^B_3, \Sigma[K]^B_3, \Delta[K]^B_2, respectively.
Assessment by time n and with certainty
5 dezembro 2017, 15:00 • José Félix Costa
Revision of topology: topological space, open, closed and clopen sets; limit points, interior and boundary of a set. Base of a topological space.
Baire topological spaces.
Caracterization of limit points in the Baire spaces. Relation between limit points and inductive scepticism. n-uniform sets.
Verification, refutation and decidability of hypotheses by time n.
Verification, refutation and decidability of hypotheses with certainty.
Vacillatory identification of sets + Parameterised scientists
28 novembro 2017, 15:00 • José Félix Costa
---- Part 1
Vacilatory TxtFex^a_b-identification. That vacilatory identification improves inductive inferring power in set identification.
TxtFex^0_ {n+1} - TxtFex*_n =\= \emptyset and TxtFex^{n+1}_ 1 - TxtFex^n_* =\= \emptyset (and other limit cases).
---- Part 2
Parameterized scientists (for sets and for functions).
That the collection of TxtEx-identifiable classes of r.e. sets is not performable by any parameterised scientist on context [.].
Set identification with errors
24 novembro 2017, 17:00 • José Félix Costa
Lifting from functions to sets and from single-valued sets to functions.
TxtEx^a- and TxtBc^a-identification, for a \in {*} \cup N. Classes TxtEx^a and TxtBc^a.
That TxtEx \subset TxtEx^1 \subset ... \subset TxtEx* (the non-collapsing character of TxtEx hierarchy).
That TxtBc \subset TxtBc^1 \subset ... \subset TxtBc* (the non-collapsing character of TxtBc hierarchy).
Structural relationships between the TxtEx and TxtBc hierarchies: TxtEx* \notin TxtBc; TxtBc \notin TxtEx*; for all n \in N, TxtEx^2n \subseteq TxtBc^n; for all n \in N, TxtEx^{2n+1} - TxtBc^n =/= \emptyset.