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Florian Pelupessy

Publications and source records attributed to Florian Pelupessy.

9 recordsLinked to original sources
arXiv2018

On $α$-largeness and the Paris-Harrington principle in $\mathrm{RCA}_0$ and $\mathrm{RCA}_0^{\displaystyle{*}}$

We examine, within $\mathrm{RCA}_0$, the treatment by Ketonen and Solovay on the use of $α$-largeness for giving an upper bound for the Paris--Harrington principle. This proof works fine in $\mathrm{RCA}_0^{\displaystyle{*}}$ for every fixed standard dimension. We also show how to modify the arguments to work within $\mathrm{RCA}_0^{\displaystyle{*}}$ for unrestricted dimensions. To the author's knowledge, this is the first time that it is confirmed that the treatment can be done within $\mathrm{EFA}$ without some transfinite induction added.

math.LO↗
arXiv2017

Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimension

We show that the well-partial orderedness of the finite downwards closed subsets of $\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $ω^{ω^ω}$. This was conjectured to be the case by Hatzikiriakou and Simpson. Since we use Friedman's adjacent Ramsey theorem for fixed dimensions in the upper bound, we also give a treatment of the reverse mathematical status of that theorem.

math.LO↗
arXiv2017

Dickson's lemma and weak Ramsey theory

We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over $\mathsf{RCA}_0^{\ast}$. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey's theorem.

math.LO↗
arXiv2017

The strength of SCT soundness

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 $\mathrm{WO}(ω_3)$ over $\mathsf{RCA_0}$

math.LO↗
arXiv2016

On "finitary" Ramsey's theorem

We examine a version of Ramsey's theorem based on Tao, Gaspar and Kohlenbach's "finitary" infinite pigeonhole principle.We will show that the "finitary" infinite Ramsey's theorem naturally gives rise to statements at the level of the infinite Ramsey's theorem, Friedman's infinite adjacent Ramsey theorem (well-foundedness of certain ordinals up to $\varepsilon_0$), $1$-consistency of theories up to PA and the finite Ramsey's theorem.

math.LO↗
arXiv2016

Phase transition results for three Ramsey-like theorems

We classify a sharp phase transition threshold for Friedman's finite adjacent Ramsey theorem. We extend the method for showing this result to two previously known classifications involving Ramsey theorem variants: the Paris--Harrington theorem and the Kanamori--McAloon theorem. We also provide tools to remove ad-hoc arguments from the proofs of phase transition results as much as currently possible.

math.LO↗
arXiv2016

Monomial ideals and independence of $\mathrm{I}Σ_2$

We show that a miniaturised version of Maclagan's theorem on monomial ideals is equivalent to $\mathrm{1}{-}\mathrm{Con}(\mathrm{I}Σ_2)$ and classify a phase transition threshold for this theorem. This work highlights the combinatorial nature of Maclagan's theorem.

math.LO↗
arXiv2016

Adjacent Ramsey theory and Higman's lemma

We show a short proof of Higman's lemma using Friedman's adjacent Ramsey theorem for pairs. This provides an alternative proof of the known upper bound for the reverse mathematical status of Higman's lemma and that of its miniaturised version.

math.LO↗