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In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017), on size-change termination in the context of Reverse Mathematics. We analyze the soundness of the SCT method. In particular, we prove that the statement any program which satisfies the combinatorial condition provided by the SCT criterion is terminating is equivalent to $mathrm{WO}(omega_3)$ over $mathsf{RCA_0}$
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion is equivalent to $Sigma^0_2$-induction over RCA$_0$.
The Gratzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show that the set of indices of computable lattices th
We determine the consistency strength of determinacy for projective games of length $omega^2$. Our main theorem is that $boldsymbolPi^1_{n+1}$-determinacy for games of length $omega^2$ implies the existence of a model of set theory with $omega + n$ W
We analyze the strength of Hellys selection theorem HST, which is the most important compactness theorem on the space of functions of bounded variation. For this we utilize a new representation of this space intermediate between $L_1$ and the Sobolev
We investigate the statement the order topology of every countable complete linear order is compact in the framework of reverse mathematics, and we find that the statements strength depends on the precise formulation of compactness. If we require tha