Parameterised scientists

28 outubro 2013, 10:30 • José Félix Costa

Parameterized scientists (for sets and for functions).

That the class of TxtEx-identifiable r.e. sets is not performable by parameterised scientist on context [.] (that the class of TxtEx-identifiable doubletons is not performable).

That the class of (TxtEx-identifiable) finite sets of non-equivalent indexes of r.e. sets is, however, performable on [.].

That the class AT of r.e. sets of indexes of recursive functions is performable on [.]f.

That the class of Ex-identifiable r.e. sets of functions is not performable on [.]f.

TxtEx-identification of r.e.s

25 outubro 2013, 14:30 • José Félix Costa

Wiehagen's theorem: on the identification of finite variants of the class of r.e. sets (= uniform class of finite variants of E).

Separation between Lang and TxtEx

21 outubro 2013, 10:30 • José Félix Costa

That K^0 is TxtEx-identifiable. (K^0 = { K \cup {x}: x \in K }.)

That K^0 \in TxtExExact.

That L \cup L', where L = {L_i: i \in N}, L_i = {0, 1, 2, ..., i}, is TxtEx-identifiable iff N \notin L'.

Non-union theorem for TxtEx.

That TxtEx is strictly included in Lang: cardinality argument.

That TxtEx is strictly included in Lang: K\star argument. (K\star = { K \cup {x}: x \in N }.)

Popperian scientists

18 outubro 2013, 14:30 • José Félix Costa

Introduction to the hierarchy of scientists: Ex, Ex^n, Ex*, Bc, Bc^n and Bc*.

Popperian scientists.

On the possibility of irrefutable, incomplete explanations.

Problem set IV.

Ends course PART I.

Non-union theorem

14 outubro 2013, 10:30 • José Félix Costa

Computational classes TxtEx and Ex. Sets AEZ (almost everywhere zero) and SD (self-describing).

Blums' non-union theorem: that Ex is not closed under union.

(Self-reference as proof technique.)

That R \not\in Ex. That PrR \in Ex (Meyer and Ritchie's theorem).

From PrR to R: Discussion around Blums' theorem and the sciences.

Identification by team of computable scientistis. (Case and Smith) That two computable scientists identify ASD^1 (almost self-describing with one anomaly), where a single scientist fails.

Exact identification. Classes TxtExExact and ExExact. That, in this context, a r.e. set L is identifiable by a scientist M iff M has a locking sequence for L.