Geodesic
Phase transitions in Proof Theory
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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Using standard methods of analytic combinatorics we elaborate critical points (thresholds) of phase transitions from provability to unprovability of arithmetical well-partial-ordering assertions in several familiar theories occurring in the reverse mathematics program. 
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     author = {Gordeev, Lev and Weiermann, Andreas},
     title = {Phase transitions in {Proof} {Theory}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
     doi = {10.46298/dmtcs.2771},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2771/}
}
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Gordeev, Lev; Weiermann, Andreas. Phase transitions in Proof Theory. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2771. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2771/

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