Homepage of Lorenzo Carlucci

Journal

L. Carlucci, A new proof-theoretic proof of the independence of Kirby-Paris' Hydra Theorem, Theoretical Computer Science 300 (2003), 365-378.
L. Carlucci, Worms, Gaps and Hydras, Mathematical Logic Quarterly, 51:4, (2005), 342-350.
L. Carlucci, S. Jain, E. Kinber, and F. Stephan, Variations on U-shaped learning. Information and Computation, 204:8, (2006), 1264-1294. Available from Science Direct here.
L. Carlucci, J. Case, S. Jain, and F. Stephan, Results on memory-limited U-shaped learning. Information and Computation, 205:10, (2007), 1551-1573. Technical report version here.
L. Carlucci, J. Case, S. Jain, and F. Stephan, Non-U-shaped vacillatory and team learning, Journal of Computer and System Sciences, 74:4, (2008), 409-430. Technical report version here.
L. Carlucci, J. Case, and S. Jain, Learning Correction Grammars, Journal of Symbolic Logic, 74:2, (2009), 489-516. Preprint here.
L. Carlucci, P. Dehornoy, and A. Weiermann, Unprovability Results involving Braids. Proceedings of the London Mathematical Society, 102(1), (2011), 159-192.
L. Carlucci, G. Lee, and A. Weiermann Sharp thresholds for hypergraph regressive Ramsey numbers. Journal of Combinatorial Theory, Series A, 118(2) (2011), 558-585.
L. Carlucci, S. Jain and F. Stephan Learning with ordinal-bounded memory from positive data Journal of Computer and System Sciences, 78, (2012), 1623-1636.
L. Carlucci and J. Case On the necessity of U-shaped learning Invited paper in Topics in Cognitive Science, 5, (2013), 56-88.
L. Carlucci, K. Zdanowski The strength of Ramsey's Theorem for coloring relatively large sets Journal of Symbolic Logic, 79:1, (2014), 89-102.
L. Carlucci, N. Galesi and M. Lauria On the Proof Complexity of Paris-Harrington and Off-Diagonal Ramsey Tautologies ACM Transactions on Computational Logic, 17(4), (2016).
L. Carlucci, A weak variant of Hindman's Theorem stronger than Hilbert's Theorem Archive for Mathematical Logic, 57 (2018), 381-389.
L. Carlucci, Weak Yet Strong restrictions of Hindman's Finite Sums Theorem Proceedings of the American Mathematical Society, 146 (2018), 819-829.
L. Carlucci, A note on Hindman-type theorems for uncountable cardinals Order, 36:1 (2019), 19-22.
L. Carlucci, L. A. Kolodziewczyk, F. Lepore, K. Zdanowski, New bounds on the strength of some restrictions of Hindman's Finite Sums Theorem, Computability, 9 (2020), 139-153.
L. Carlucci, M. Lauria, Upper bounds on positional Paris-Harrington games, Discrete Mathematics, vol. 344, issue 3, (2021).
L. Carlucci, D. Tavernelli, Hindman's Theorem for sums along the full binary tree, Sigma^0_2-induction and the Pigeonhole Principle for trees, Archive for Mathematical Logic (2022). https://doi.org/10.1007/s00153-021-00814-2. (Online version here).
L. Carlucci, D. F. Breton, The Adjacent Hindman's Theorem for uncountable groups, Colloquium Mathematicum, vol. 173, no. 2, (2023). (Online version here).
L. Carlucci, L. Mainardi, Regressive variants of Hindman's theorem, Archive for Mathematical Logic, vol. 67, (2024), 447-472. (Online version here).

Conference

L. Carlucci, Provably Total Functions and the Hydra Game, The Bulletin of Symbolic Logic, vol. 9, no. 1, pg. 89, March 2003.
L. Carlucci, S. Jain, E. Kinber, and F. Stephan, Variations on U-shaped learning . In Peter Auer, Ron Meir, editors, Learning Theory, Proceedings of the 18th Annual Conference on Learning Theory, COLT 2005. Lecture Notes in Computer Science n. 3559, pages 382-397, Springer.
L. Carlucci, J. Case, S. Jain, and F. Stephan, Non U-shaped Vacillatory and Team Learning . In S. Jain, H. U. Simon and E. Tomita, editors, Algorithmic Learning Theory, 16th International Conference, ALT 2005, Singapore, October 2005, pages 241-255. Lecture Notes in Artificial Intelligence 3734. Springer Verlag, 2005.
L. Carlucci, J. Case, S. Jain, and F. Stephan, Memory-Limited U-shaped Learning. In Gabor Lugosi and Hans Ulrich Simon, editors, Proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, pages 244-258. Lecture Notes in Artificial Intelligence 4005, Springer Verlag, 2006.
L. Carlucci, J. Case, and S. Jain, Learning Correction Grammars, in Nader Bshouty and Claudio Gentile, editors, Proceedings of the 20th Annual Conference on Learning Theory, COLT 2007, San Diego, USA, 2007, pages 203-217, Lecture Notes in Computer Science 4539, Springer Verlag, 2007.
L. Carlucci, Incremental learning with ordinal bounded example memory, In Ricard Gavalda, Gabor Lugosi, Thomas Zeugmann, and Sandra Zilles, editors, Proceedings of the The 20th International Conference on Algorithmic Learning Theory, ALT 2009, Porto, Portugal, 2009, pages 323-337, Lecture Notes in Artificial Intelligence 5809, Springer Verlag, 2009.
L. Carlucci, N. Galesi, M. Lauria, Paris-Harrington Tautologies, in (eds.), Proceedings of IEEE Conference on Computational Complexity 2011, CCC 2011, San Jose, USA, 2011, 93- 103.
L. Carlucci, K. Zdanowski, A note on Ramsey Theorems and Turing Jumps, Proceedings of the Turing Centenary Conference, CiE 2012, Cambridge, UK, 2012.
L. Carlucci, L. A. Kolodziewczyk, F. Lepore, K. Zdanowski, New bounds on restrictions of Hindman's Finite Sums Theorem, In J. Kari, F. Manea, and I. Petre, (editors), Unveiling Dynamics and Complexity, 13th Conference Computability in Europe 2017 (Turku, Finland, June 12-16, 2017), Springer, 2017, pp. 210-220.
L. Carlucci, L. Mainardi, M. Rathjen, A Note on the Ordinal Analysis of RCA₀+WO(σ), Proceedings of CiE 2019, Durham, UK, 2019, pp. 144-155.
L. Carlucci, Restrictions of Hindman's Theorem: An Overview, In: De Mol L., Weiermann A., Manea F., Fernandez-Duque D. (eds), Connecting with Computability. CiE 2021. Lecture Notes in Computer Science, vol 12813, pp. 94-105.

Preprints

Reductions of well-ordering principles to combinatorial theorems. (with Leonardo Mainardi and Konrad Zdanowski).

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