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math.LO2026
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…
math.LO2025
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…
math.LO2024
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…