Truth-table reductions and minimum sizes of forcing conditions : preliminary draft(Proof Theory of Arithmetic)
Masahiro Kumabe, Toshio Suzuki, Takeshi Yamazaki · Kyoto University Research Information Repository (Kyoto University) · 2007
This note is a refinement of our former note [KSY05] $u_{\mathrm{L}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{m}\mathrm{i}\mathrm{c}}$truth-table reductions and minimum sizes of forcing conditions (preliminary draft)"Surikats $eb$ -kenkyusho $K\overline{o}ky\overline{u}roku$ 1442 (2005), 42-47.The current note extends and corrects [KSY05].In our former works, for a given concept of reduc- tion, we study the $\mathrm{f}\mathrm{o}\mathrm{U}\mathrm{o}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{g}$ hypothesis: "For a random oracle $A$ , with proba- bility one, the degree of the one-query tautologies with respect to $A$ is strictly higher than the degree of A." In our former works, the following three results 'Corresponding author.