Fernando Ferreira (Universidade de Lisboa)

The finite convergence principle - some logical observations

Two years ago, Terence Tao wrote in his blog an essay entitled "Soft analysis, hard analysis, and the finite convergence principle." In this essay, Tao speaks informally of the notions of "soft" analysis and "hard" analysis. He sustains that results of abstract ("soft") analysis may hide deep ("hard") computational or combinatorial information and that it is worthwhile to bring out explicitly this information. He denotes this process as the finitization of the qualitative results. Tao discusses in his blog the finitization of the following well known "soft" principle from undergraduate analysis: every bounded monotone sequence of real numbers converges. We explain this finitization and draw some connections with a logical (so-called functional) interpretation that stems from Kurt Gödel's last published paper of 1958. We finish the presentation by making a few observations regarding this novel interpretation.