4 papers · 1 filter
The cohesive and stable Ramsey theorems and proof size over a weak base theory
Leszek Aleksander KoÅodziejczyk, Mengzhou Sun
We show that over the weak base theory , cohesive Ramsey's theorem for pairs implies exponential closure of the definable cut ,…
Robinson Splitting Theorem and Induction
Yong Liu, Cheng Peng, Mengzhou Sun
The Robinson Splitting Theorem states that a c.e. degree splits over any low c.e. degree . We prove that a weaker version of this theorem holds…
The finite cohesiveness principle
Mengzhou Sun
We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result sho…
The Kaufmann--Clote question on end extensions of models of arithmetic and the weak regularity principle
Mengzhou Sun
We investigate the end extendibility of models of arithmetic with restricted elementarity. By utilizing the restricted ultrapower construction in the second-order context, for each…