8 papers
The Limits of Arithmetical Pluralism: Incompleteness, Large Cardinals, and Graded Non-Pluralism
Yong Cheng
Gödelian incompleteness yields arithmetical sentences such that and are both consistent. Are such extensions equally legitimate? I propose graded epistemic a…
On the depth of Wiles's proof of Fermat's Last Theorem
Yong Cheng, Colin McLarty
What constitutes depth in a mathematical proof? This paper addresses this foundational question through a close case study of Andrew Wiles's proof of Fermat's Last Theorem. We prop…
On Rosser theories
Yong Cheng
Rosser theories play an important role in the study of the incompleteness phenomenon and meta-mathematics of arithmetic. In this paper, we first define the notions of -Rosser th…
The limitless First Incompleteness Theorem
Yong Cheng
This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem (). A natural question is: can we find a minimal theory…
Current research on Gödel's incompleteness theorems
Yong Cheng
We give a survey of current research on Gödel's incompleteness theorems from the following three aspects: classifications of different proofs of Gödel's incompleteness theorems, th…
On the depth of Gödel's incompleteness theorem
Yong Cheng
In this paper, we use Gödel's incompleteness theorem as a case study for investigating mathematical depth. We take for granted the widespread judgment by mathematical logicians tha…