Pre-prints can be found on the arXiv, while a recent Zoom talk in the UConn logic colloquium may be found here.

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Published papers are as follows:

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[64] Sam Sanders, Connecting real and hyperarithmetical analysis, to appear in Documenta Mathematica, 26 pages, arxiv: https://arxiv.org/abs/2408.13760.

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[63] Dag Normann and Sam Sanders, On the computational properties of open sets, to appear in Journal of Logic and Computation,  33 pages, arxiv: https://arxiv.org/abs/2203.05250.

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[62] Dag Normann and Sam Sanders, On the logical and computational properties of the Vitali covering theorem, Annals of Applied Logic, 39 pages, arxiv: https://arxiv.org/abs/1902.02756.

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[61] Sam Sanders, A note on continuous functions on metric spaces, to appear in the Bulletin of Symbolic Logic, 17 pages, arxiv: https://arxiv.org/abs/2404.06805.

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[60] Sam Sanders, Approximation theorems throughout Reverse Mathematics, to appear in the Journal of Symbolic Logic, arxiv: https://arxiv.org/abs/2311.11036, 23 pages.

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[59] Sam Sanders, On the computational properties of decompositions of continuity, LNCS 14773,  proceedings of CiE24, Springer, 12 pages, 2024.

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[58] Sam Sanders, Exploring the Abyss in Kleene computability theory, to appear in Computability, 22 pages, arxiv: https://arxiv.org/abs/2308.07438.

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[57] Sam Sanders, Big in Reverse Mathematics: measure and category, Journal of Symbolic Logic, 44 pages, arxiv:  https://arxiv.org/abs/2303.00493 and doi: https://doi.org/10.1017/jsl.2023.65.

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[56] Dag Normann and Sam Sanders, The Biggest Five of Reverse Mathematics, to appear in Journal of Mathematical Logic, 40 pages, arxiv:  https://arxiv.org/abs/2212.00489 and doi: https://doi.org/10.1142/S0219061324500077.

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[55] Sam Sanders,   Big in Reverse Mathematics: the uncountability of the reals, Journal of Symbolic Logic, 28 pages, arxiv: https://arxiv.org/abs/2208.03027 and doi:  https://doi.org/10.1017/jsl.2023.42.

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[54] Sam Sanders, The non-normal abyss in Kleene’s computability theory, LNCS, proceedings of CiE2023 pp. 12, arxiv: https://arxiv.org/abs/2302.07066 or doi: https://doi.org/10.1007/978-3-031-36978-0_4.

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[53] Jacques Bair, Alexandre Borovik, Vladimir Kanovei, Mikhail G. Katz, Semen S. Kutateladze, Sam Sanders, David Sherry, Monica Ugaglia and Mark van Atten. Is Pluralism in the History of Mathematics Possible?. Math Intelligencer 45, 8 (2023), https://doi.org/10.1007/s00283-022-10248-0.

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[52] Dag Normann and Sam Sanders, On robust theorems due to Bolzano, Weierstrass, Jordan, and Cantor, to appear in: Journal of Symbolic Logic, pp. 44, arxiv: https://arxiv.org/abs/2102.04787. DOI: 10.1017/jsl.2022.71.

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[51] Jacques Bair, Alexandre Borovik, Vladimir Kanovei, Mikhail G. Katz, Semen S. Kutateladze, Sam Sanders, David Sherry, and
Monica Ugaglia, Historical Infinitesimalists and Modern Historiography of Infinitesimals,  Antiquitates Mathematicae, vol. 16 (1) 2022, p. 189–256.

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[50] Dag Normann and Sam Sanders, On the computational properties of basic mathematics notions, to appear in: Journal of Logic and Computation, pp. 43, arxiv: https://arxiv.org/abs/2203.05250. DOI: 10.1093/logcom/exac075.

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[49] Sam Sanders, On the computational properties of the uncountability of $\mathbb{R}$,  LNCS 13468,  Proceedings of WoLLIC2022, pp. 16, arxiv: https://arxiv.org/abs/2206.12721.

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[48] Sam Sanders, Reverse Mathematics of the uncountability of $\mathbb{R}$, LNCS 13359,  Proceedings of CiE22, pp. 12, arxiv: https://arxiv.org/abs/2203.05292.

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[47] Dag Normann and Sam Sanders, On the uncountability of $\mathbb{R}$, Journal of Symbolic Logic, pp. 40, arxiv: https://arxiv.org/abs/2007.07560, DOI: 10.1017/jsl.2022.27.

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[46] Sam Sanders, Between Turing and Kleene,  LNCS 13137,  Proceedings of LFCS22, 2022, pp 20, arxiv: https://arxiv.org/abs/2111.05052.

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[45] Dag Normann and Sam Sanders, Betwixt Turing and Kleene,  LNCS 13137,  Proceedings of LFCS22, 2022, pp 18, arxiv: https://arxiv.org/abs/2109.01352.

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[44] Sam Sanders, Representations and the foundations of mathematics, Notre Dame J. Formal Logic 63(1), 1-28, Duke University Press, 2022/2, arxiv: https://arxiv.org/abs/1910.07913.

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[43] Sam Sanders, Countable sets versus sets that are countable in Reverse Mathematics, Computability, vol. 11, no. 1, pp. 9-39, 2022, arxiv: https://arxiv.org/abs/2011.01772.

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[42] Sam Sanders, Splittings and robustness for the Heine-Borel theorem, LNCS 12813, Proceedings of Computability in Europe  (CIE), Springer, 2021.

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[41] Dag Normann and Sam Sanders, The Axiom of Choice in Computability Theory and Reverse Mathematics, with a cameo for the Continuum Hypothesis, Journal of Logic and Computation, Volume 31, Issue 1, January 2021, Pages 297–325, https://doi.org/10.1093/logcom/exaa080

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[40] Sam Sanders, Lifting countable to uncountable mathematics, to appear in: Information and Computation  (2020) arxiv: https://arxiv.org/abs/1908.05677 and https://doi.org/10.1016/j.ic.2021.104762.

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[39] Sam Sanders, Reverse Mathematics of topology: dimension, paracompactness, and splittings, Notre Dame J. Formal Logic 61 (4) 537 - 559, November 2020.

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[38] Dag Normann and Sam Sanders, Open sets in computability theory and Reverse Mathematics, Journal of Logic and Computation, Volume 30, Issue 8 (2020), arXiv: https://arxiv.org/abs/1910.02489.

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[37] Dag Normann and Sam Sanders Pincherle’s theorem in Reverse Mathematics and computability theory, Annals of Pure and Applied Logic, Volume 171, Issue 5, May 2020, 102788, arXiv: https://arxiv.org/abs/1808.09783, https://doi.org/10.1016/j.apal.2020.102788 (2020).

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[36] Sam Sanders, The unreasonable effectiveness of Nonstandard Analysis,  The Journal of Logic and Computation, Volume 30, Issue 1 (2020), pages 459–524, arxiv: https://arxiv.org/abs/1508.07434.

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[35] Sam Sanders, Nets and Reverse Mathematics: a pilot study,  Computability, vol. 10, no. 1, pp. 31-62, 2021, arxiv: https://arxiv.org/abs/1905.04058 (2019), pp. 34.

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[34] Sam Sanders, Lifting recursive counterexamples to higher-order arithmetic, Proceedings of LFCS2020, Lecture Notes in Computer Science (LNCS), Springer (2019).

[33] Dag Normann and Sam Sanders, The strength of compactness in Computability Theory and Nonstandard Analysis, Annals of Pure and Applied Logic, Volume 170, Issue 11, November 2019, 102710

[32] Sam Sanders, Splittings and disjunctions in Reverse Mathematics, Notre Dame J. Formal Logic 61(1): 51-74 (January 2020). DOI: 10.1215/00294527-2019-0032.

[31] Dag Normann and Sam Sanders, On the mathematical and foundational significance of the uncountable, Journal for Mathematical Logic, Vol. 19, No. 01, 1950001 (2019), arXiv: https://arxiv.org/abs/1711.08939 (2019).

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[30] Dag Normann and Sam Sanders, Computability theory, Nonstandard Analysis, and their connections, The Journal of Symbolic Logic, 84(4), 1422-1465. doi:10.1017/jsl.2019.69, arXiv: https://arxiv.org/abs/1702.06556 (2019).

[29], Sam Sanders, Nets and Reverse Mathematics, LNCS proceedings of CiE2019, Springer (2019).

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[28] Sam Sanders, On the computability theory and reverse mathematics of domain theory, LNCS proceedings of WoLLIC2019, Springer (2019).

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[27] Sam Sanders, A note on non-classical Nonstandard Arithmetic, Annals of Pure and Applied Logic, Volume 170, Issue 4, April 2019, Pages 427-445 , https://arxiv.org/abs/1805.11705 (2018).

[26] Benno van den Berg and Sam Sanders, Pamameter-free and Reverse Mathematics, Annals of Pure and Applied Logic, Annals of Pure and Applied Logic 170 (3), 273-296, 2019 http://arxiv.org/abs/1409.6881

[25] Boris Katz, Mikhail Katz, and Sam Sanders, A footnote to The crisis in contemporary mathematics, Historia Mathematica 2018, https://doi.org/10.1016/j.hm.2018.03.002.

[24], Sam Sanders, Refining the taming of the Reverse Mathematics zoo, Notre Dame Journal of Formal Logic 59 (2018), 579-597.

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[23] Sam Sanders, Some nonstandard equivalences in Reverse Mathematics, LNCS, Springer, Computability in Europe (CiE) 2018.

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[22], Sam Sanders, Metastability and Higher-order Computability Theory, LNCS, Springer, Logical Foundations of Computer Science (LFCS) 2018.

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[21] Sam Sanders, The Gandy-Hyland functional and a hitherto unknown computational aspect of Non- standard Analysis, Accepted for publication in Computability, http://arxiv.org/abs/1502. 03622 (2017).

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[20] Sam Sanders, To be or not to be constructive, Special issue of Indagationes Mathematicae titled L.E.J. Brouwer, fifty years later, doi:10.1016/j.indag.2017.05.005 (2017), pp. 69.

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[19] Peter Fletcher, Karel Hrbacek, Kanovei Vladimir, Mikhail G. Katz, Claude Lobry, and Sam Sanders, Approaches To Analysis With Infinitesimals Following Robinson, Nelson, And Oth- ers, Real Analysis Exchange, arXiv: https://arxiv.org/abs/1703.00425 (2017).

[18] Sam Sanders, Formalism16, Synthese, special issue on logic and the foundations of mathe- matics, doi:10.1007/s11229-017-1322-2, 2017, pp. 1–48.

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[17] Sam Sanders, Grilliot’s trick in Nonstandard Analysis, Logical Methods in Computer Science, Special Issue for CCC15 (2017).

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[16] Sam Sanders, From Nonstandard Analysis to various flavours of Computability Theory, Proceedings of TAMC17, Lecture Notes in Computer Science 10185, Springer (2017).

[15] Kristina Liefke and Sam Sanders, A computable solution to Partee’s temperature puzzle, Proceedings of LACL2016 (Logical Aspects of Computational Linguistics), Lecture Notes in Computer Science 10054, Springer (2016), 175–190.

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[14] Kristina Liefke and Sam Sanders, A computable solution to Partee’s temperature puzzle, NLCS (Natural Language and Computer Science), satellite workshop of LICS2016, http://www.indiana.edu/~iulg/nlcs.html (2016).

[13] Sam Sanders, The computational content of Nonstandard Analysis, Electronic Proceedings in Computer Science 213, Classic Logic and Computation, Porto (CL&C2016) (2016), 21-40.

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[12] Sam Sanders, Algorithm and Proof as Ω-invariance and Transfer: A new model of computation in Nonstandard Analysis, Electronic Proceedings in Computer Science, DCM2012 143 (2014), 97–109.

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[11] Sam Sanders, On algorithm and robustness in a non-standard sense, New challenges to philosophy of science, Philos. Sci. Eur. Perspect., vol. 4, Springer, Dordrecht, 2013, pp. 99–112.

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[10] Sam Sanders, On the connection between nonstandard analysis and constructive analysis, Logique et Anal. (N.S.) 56 (2013), no. 222, 183–210.

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[9] Sam Sanders, Reverse-engineering reverse mathematics, Ann. Pure Appl. Logic 164 (2013), no. 5, 528–541.

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[8] Sam Sanders and Keita Yokoyama, The Dirac delta function in two settings of reverse mathematics, Arch. Math. Logic 51 (2012), no. 1-2, 99–121.

[7] Sam Sanders, Reverse mathematics & nonstandard analysis: towards a dispensability argument, Proceedings of the Ontology conference, Keio University press, 2011, pp. 11.

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[6] Sam Sanders, ERNA and Friedman’s reverse mathematics, J. Symbolic Logic 76 (2011), no. 2, 637–664.

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[5] Sam Sanders, Relative arithmetic, MLQ Math. Log. Q. 56 (2010), no. 6, 564–572.

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[4] Sam Sanders, More infinity for a better finitism, Ann. Pure Appl. Logic 161 (2010), no. 12, 1525–1540.

[3] Chris Impens and Sam Sanders, Saturation and Σ2-transfer for ERNA, J. Symbolic Logic 74 (2009), no. 3, 901–913.

 

[2] Chris Impens and Sam Sanders, Transfer and a supremum principle for ERNA, J. Symbolic Logic 73 (2008), no. 2, 689–710.

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[1]  Chris Impens and Sam Sanders, ERNA at work, The strength of nonstandard analysis, Springer, 2007, pp. 64–75.

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