Sharif Digital Repository

In this thesis, we provide a comprehensive overview of the efforts made towards achieving the goals of Hilbert’s program, and evaluate how successful They are. We begin by discussing Gödel’s incompleteness theorems, and then as a first attempt we present a brief presentation of Gentzen’s consistency theorem. Subsequently, various research fields that branched out from these initial efforts are explored, encompassing the application of the Omega-Rule, reverse mathematics, and self-verifying systems. Furthermore, we present the concept of “Almost Finitistic Consistency” as an alternative approach within Hilbert’s program. In conclusion, a thorough assessment of the success of Hilbert’s program...