How unprovable is Rabin's decidability theorem?

Leszek Aleksander Kolodziejczyk, Henryk Michalewski. How unprovable is Rabin's decidability theorem?. In Martin Grohe, Eric Koskinen, Natarajan Shankar, editors, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016. pages 788-797, ACM, 2016. [doi]

@inproceedings{KolodziejczykM16,
  title = {How unprovable is Rabin's decidability theorem?},
  author = {Leszek Aleksander Kolodziejczyk and Henryk Michalewski},
  year = {2016},
  doi = {10.1145/2933575.2934543},
  url = {http://doi.acm.org/10.1145/2933575.2934543},
  researchr = {https://researchr.org/publication/KolodziejczykM16},
  cites = {0},
  citedby = {0},
  pages = {788-797},
  booktitle = {Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016},
  editor = {Martin Grohe and Eric Koskinen and Natarajan Shankar},
  publisher = {ACM},
  isbn = {978-1-4503-4391-6},
}