Seminários de Lógica Matemática

14 de Maio 2009, 18h00

Strict-Pi^1_1-reflection - bounded sets vs finite sequences (part 2)
Complexo Interdisciplinar, Sala B3-01

ANTÓNIO FERNANDES (IST - Universidade Técnica de Lisboa, CMAF - UL)

Abstract:

Strict-Pi^1_1-reflection is a principle originally introduced by Barwise in the context of weak set theory. In 1996, Andrea Cantini studied the same principle in the context of feasible arithmetic and conjectured that it is equivalent to the weak König's lemma (WKL) modulo a weak theory. We will describe a conservation result that is the counterpart of an analogous result involving WKL, and isolate a criterium that can help do disprove Cantini's conjecture (if it can be disproved, of course!). One consequence of such a result is that, the notions of bounded set and binary sequence differ essentially in this weak setting (the former being stronger).

This way the principle of strict-Pi^1_1-reflection would be a better replacement for WKL on formalizing analysis in systems of feasible arithmetic.

| back