{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T22:40:10Z","timestamp":1710024010912},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,2,3]],"date-time":"2009-02-03T00:00:00Z","timestamp":1233619200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nat Comput"],"published-print":{"date-parts":[[2009,9]]},"DOI":"10.1007\/s11047-009-9114-3","type":"journal-article","created":{"date-parts":[[2009,2,2]],"date-time":"2009-02-02T08:07:54Z","timestamp":1233562074000},"page":"499-516","source":"Crossref","is-referenced-by-count":19,"title":["General relativistic hypercomputing and foundation of mathematics"],"prefix":"10.1007","volume":"8","author":[{"given":"Hajnal","family":"Andr\u00e9ka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Istv\u00e1n","family":"N\u00e9meti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P\u00e9ter","family":"N\u00e9meti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,2,3]]},"reference":[{"key":"9114_CR4","unstructured":"Andr\u00e9ka H, N\u00e9meti I (2007) Relativistic computers and Hilbert\u2019s Program for mathematics. Manuscript"},{"key":"9114_CR2","doi-asserted-by":"crossref","unstructured":"Andr\u00e9ka H, Madar\u00e1sz JX, N\u00e9meti I, with contributions from Andai A, Sain I, S\u00e1gi G, T\u0151ke Cs, V\u00e1lyi S (2000) On the logical structure of relativity theories. Internet book, Budapest. http:\/\/www.math-inst.hu\/pub\/algebraic-logic\/olsort.html","DOI":"10.1007\/978-94-017-0452-6_3"},{"key":"9114_CR1","doi-asserted-by":"crossref","unstructured":"Andr\u00e9ka H, Madar\u00e1sz JX, N\u00e9meti I (2007) Logic of spacetime and relativity theory. In: Aiello M, van Benthem J, Pratt-Hartman I (eds) Handbook of spatial logics. Springer-Verlag, pp 607\u2013711","DOI":"10.1007\/978-1-4020-5587-4_11"},{"issue":"2","key":"9114_CR3","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s11225-008-9125-6","volume":"89","author":"H Andr\u00e9ka","year":"2008","unstructured":"Andr\u00e9ka H, Madar\u00e1sz JX, N\u00e9meti I, Sz\u00e9kely G (2008a) Axiomatizing relativistic dynamics without conservation postulates. Studia Logica 89(2):163\u2013186","journal-title":"Studia Logica"},{"issue":"9","key":"9114_CR5","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10714-007-0577-1","volume":"40","author":"H Andr\u00e9ka","year":"2008","unstructured":"Andr\u00e9ka H, N\u00e9meti I, W\u00fcthrich (2008b) A twist in the geometry of rotating black holes: seeking the cause of acausality. Gen Relativ Gravitat 40(9):65\u201389","journal-title":"Gen Relativ Gravitat"},{"key":"9114_CR6","unstructured":"Barrow JD (2005) How to do an infinite number of things before breakfast. New Scientist, 29 January 2005"},{"key":"9114_CR7","unstructured":"Barrow JD, Tipler FJ (1986) The anthropic cosmological principle. Oxford University Press, UK"},{"key":"9114_CR8","unstructured":"Chown M (2002) Smash and grab. New Scientist, 6 April 2002, pp 24\u201328"},{"key":"9114_CR9","doi-asserted-by":"crossref","unstructured":"Cooper SB (2006) How can nature help us compute? In: Wiedermann J, Stuller J, Tel G, Pokorny J, Bielikova M, (eds) SOFSEM 2006: theory and practice of computer science\u201432nd conference on current trends in theory and practice of computer science, Merin, Czech Republic, January 2006. Springer lecture notes in computer science no. 3831, pp 1\u201313","DOI":"10.1007\/11611257_1"},{"key":"9114_CR10","unstructured":"D\u00e1vid Gy (2005) Modern cosmology\u2014astronomical, physical and logical approaches. Abstracts for the conference \u201cLogic in Hungary 2005\u201d. http:\/\/atlas-conferences.com\/cgi-bin\/abstract\/caqb-64"},{"key":"9114_CR11","doi-asserted-by":"crossref","unstructured":"Earman J (1995) Bangs, crunches, whimpers, shrieks. Singularities and acausalities in relativistic spacetimes. Oxford University Press, Oxford","DOI":"10.1093\/oso\/9780195095913.001.0001"},{"key":"9114_CR12","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1086\/289716","volume":"60","author":"J Earman","year":"1993","unstructured":"Earman J, Norton J (1993) Forever is a day: supertasks in Pitowsky and Malament-Hogarth spacetimes. Philos Sci 60 :22\u201342","journal-title":"Philos Sci"},{"key":"9114_CR13","volume-title":"Paul Benacerraf: the Philosopher and his critics","author":"J Earman","year":"1994","unstructured":"Earman J, Norton J (1994) Infinite pains: the trouble with supertasks. In: Stich S (ed) Paul Benacerraf: the Philosopher and his critics. Blackwell, New York"},{"key":"9114_CR14","doi-asserted-by":"crossref","unstructured":"Etesi G (2002) Note on a reformulation of the strong cosmic censor conjecture based on computability. Phys Lett B 550:1\u20137. Revised version (2008)","DOI":"10.1016\/S0370-2693(02)02966-0"},{"issue":"2","key":"9114_CR15","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1023\/A:1014019225365","volume":"41","author":"G Etesi","year":"2002","unstructured":"Etesi G, N\u00e9meti I (2002) Turing computability and Malament-Hogarth spacetimes. Int J Theor Phys 41(2):342\u2013370","journal-title":"Int J Theor Phys"},{"key":"9114_CR16","first-page":"261","volume-title":"Kurt G\u00f6del collected works","author":"K G\u00f6del","year":"1995","unstructured":"G\u00f6del K (1995) Lecture on rotating universes. In: Feferman S, Dawson JS, Goldfarb W, Parson C, Solovay RN (eds) Kurt G\u00f6del collected works, vol 3. Oxford University Press, New York, pp 261\u2013289"},{"key":"9114_CR17","unstructured":"Gyenis B, Roberts B (2007) Supertasks: G\u00f6del strikes back. Preprint, Department of History and Philosophy of Science, University of Pittsburgh"},{"key":"9114_CR18","doi-asserted-by":"crossref","unstructured":"Hogarth ML (1994) Non-Turing computers and non-Turing computability. In: Hull D, Forbes M, Burian RM (eds) PSA 1994, vol 1. Philosophy of Science Association, East Lansing, pp 126\u2013138","DOI":"10.1086\/psaprocbienmeetp.1994.1.193018"},{"key":"9114_CR19","unstructured":"Hogarth ML (2000) Predictability, computability, spacetime. PhD Dissertation, University of Cambridge, UK. http:\/\/ftp.math-inst.hu\/pub\/algebraic-logic\/Hogarththesis.ps.gz"},{"key":"9114_CR20","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1093\/bjps\/55.4.681","volume":"55","author":"ML Hogarth","year":"2004","unstructured":"Hogarth ML (2004) Deciding arithmetic using SAD computers. Br J Philos Sci 55:681\u2013691","journal-title":"Br J Philos Sci"},{"key":"9114_CR21","unstructured":"Kalm\u00e1r L (1959) An argument against the plausibility of Church\u2019s thesis. In: Heyting A (ed) Constructivity in mathematics. North-Holland, Amsterdam"},{"key":"9114_CR23","unstructured":"Loff B, Costa JF (2009) Five views of hypercomputation. Int J Unconv Comput, Special Issue on Hypercomputation (in print)"},{"key":"9114_CR26","unstructured":"Madar\u00e1sz JX, Sz\u00e9kely G (2005) The effects of gravitation on clocks, proved in axiomatic relativity. Abstracts for the conference \u201cLogic in Hungary 2005\u201d, http:\/\/atlas-conferences.com\/cgi.bin\/abstract.caqb-41"},{"issue":"5","key":"9114_CR24","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s10701-005-9041-9","volume":"36","author":"JX Madar\u00e1sz","year":"2006","unstructured":"Madar\u00e1sz JX, N\u00e9meti I, Sz\u00e9kely G (2006) Twin Paradox and the logical foundation of space-time. Found Phys 36(5):681\u2013714. arXiv:gr-qc\/0504118","journal-title":"Found Phys"},{"key":"9114_CR25","doi-asserted-by":"crossref","unstructured":"Madar\u00e1sz JX, N\u00e9meti I, Sz\u00e9kely G (2007) First-order logic foundation of relativity theories. In: Mathematical problems from applied logic II. International Mathematical Series, vol 5, Springer-Verlag, New York, pp 217\u2013252","DOI":"10.1007\/978-0-387-69245-6_4"},{"key":"9114_CR27","unstructured":"Malament D (1988) Private communication to Earman, J., Cf. Earman\u2019s book in the present list of references, p 238"},{"key":"9114_CR28","unstructured":"N\u00e9meti I (1965) Computing the disturbance of phone lines caused by high-voltage electrical power lines. Master Thesis, Department of Electrodynamics, Technical University Budapest"},{"key":"9114_CR29","unstructured":"N\u00e9meti I (1987) On logic, relativity, and the limitations of human knowledge. Iowa State University, Department of Mathematics, Ph.D. course during the academic year 1987\/88"},{"key":"9114_CR30","doi-asserted-by":"crossref","unstructured":"N\u00e9meti I, Andr\u00e9ka H (2006) Can general relativistic computers break the Turing barrier? In: Beckmann A, Berger U, L\u00f6we B, Tucker JV (eds) Logical approaches to computational barriers, second conference on computability in Europe, CiE 2006, Swansea, UK. Proceedings, lecture notes in computer science 3988, Springer-Verlag, Berlin, pp 398\u2013412","DOI":"10.1007\/11780342_42"},{"key":"9114_CR31","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.amc.2005.09.075","volume":"178","author":"I N\u00e9meti","year":"2006","unstructured":"N\u00e9meti I, D\u00e1vid Gy (2006) Relativistic computers and the Turing barrier. J Appl Math Comput 178:118\u2013142","journal-title":"J Appl Math Comput"},{"key":"9114_CR32","volume-title":"The geometry of Kerr black holes","author":"B O\u2019Neill","year":"1995","unstructured":"O\u2019Neill B (1995) The geometry of Kerr black holes. A K Peters, Wellesley"},{"key":"9114_CR33","unstructured":"Ori A (1997) On the traversability of the Cauchy horizon: Herman and Hiscock\u2019s argument revisited. In: Ori A, Ori LM (eds) Internal structures of black holes and spacetime singularitites. Ann Isra Phys Soc 13, IOP"},{"key":"9114_CR34","first-page":"81","volume":"39","author":"I Pitowsky","year":"1990","unstructured":"Pitowsky I (1990) The physical Church thesis and physical computational complexity. Iyyun A Jerus Philos Q 39:81\u201399","journal-title":"Iyyun A Jerus Philos Q"},{"key":"9114_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-21717-7","volume-title":"Computability in analysis and physics","author":"MB Pour-El","year":"1989","unstructured":"Pour-El MB, Richards JI (1989) Computability in analysis and physics. Springer-Verlag, Berlin"},{"key":"9114_CR36","unstructured":"Reynolds CC, Brenneman LW, Garofalo D (2004) Black hole spin in AGN and GBHCs. Oct. 5. arXiv:astro-ph\/0410116 (Evidence for rotating black holes)"},{"key":"9114_CR37","unstructured":"S\u00e1gi G, Etesi G (2005) Transfinite computations and diameters of spacetimes.Hungarian Academy of Sciences, Budapest"},{"key":"9114_CR38","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1023\/A:1021365222692","volume":"13","author":"O Shagrir","year":"2003","unstructured":"Shagrir O, Pitowsky I (2003) Physical hypercomputation and the Church-Turing Thesis. Minds Mach 13:87\u2013101","journal-title":"Minds Mach"},{"key":"9114_CR39","unstructured":"Strohmayer TE (2001) Discovery of a 450 HZ quasi-periodic oscillation from the microquasar GRO J1655-40 with the Rossi X-Ray timing explorer. Astrophys J 553(1):L49\u2013L53. (Evidence for rotating black holes.) arXiv:astro-ph\/0104487"},{"key":"9114_CR50","doi-asserted-by":"crossref","unstructured":"Syropoulos A (2008) Hypercomputation. Springer","DOI":"10.1007\/978-0-387-49970-3"},{"key":"9114_CR40","volume-title":"Black holes","author":"EF Taylor","year":"2000","unstructured":"Taylor EF, Wheeler JA (2000) Black holes. Addison-Wesley, Longman, San Francisco"},{"key":"9114_CR41","doi-asserted-by":"crossref","unstructured":"Tegmark M (2003) Parallel universes. Scientific American, May 2003, pp 41\u201351","DOI":"10.1038\/scientificamerican0503-40"},{"key":"9114_CR42","volume-title":"The physics of immortality","author":"FJ Tipler","year":"1994","unstructured":"Tipler FJ (1994) The physics of immortality. Anchor Books, New York"},{"key":"9114_CR22","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1007\/978-3-642-56478-9_30","volume-title":"Mathematics unlimited\u20142001 and beyond","author":"J Leeuwen van","year":"2001","unstructured":"van Leeuwen J, Wiedermann J (2001) The Turing Machine paradigm in comtemporary computing. In Enquist B, Schmid W (eds) Mathematics unlimited\u20142001 and beyond. Springer-Verlag, Berlin, pp. 1139\u20131155"},{"key":"9114_CR43","doi-asserted-by":"crossref","DOI":"10.7208\/chicago\/9780226870373.001.0001","volume-title":"General relativity","author":"RM Wald","year":"1984","unstructured":"Wald RM (1984) General relativity. University of Chicago Press, Chicago"},{"key":"9114_CR44","doi-asserted-by":"crossref","unstructured":"Welch PD (2008) On the extent of computation in Malament-Hogarth spacetimes. Brit J Philos Sci 59(4): 659\u2013674. arXiv:gr-qc\/0609035v1","DOI":"10.1093\/bjps\/axn031"},{"key":"9114_CR45","first-page":"287","volume-title":"UMC 2002 Lecture notes in computer science, vol 2509","author":"J Wiedermann","year":"2002","unstructured":"Wiedermann J, van Leeuwen J (2002) Relativistic computers and non-uniform complexity theory. In: Calude et\u00a0al (eds) UMC 2002 Lecture notes in computer science Vol 2509. Springer-Verlag, Berlin, pp. 287\u2013299"},{"key":"9114_CR46","unstructured":"Wischik L (1997) A formalization of non-finite computation. Dissertation for the degree of Master of Philosophy, University of Cambridge. http:\/\/www.wischik.com\/lu\/philosophy\/non-finite-computation.html"}],"container-title":["Natural Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-009-9114-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11047-009-9114-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-009-9114-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T22:11:34Z","timestamp":1710022294000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11047-009-9114-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,3]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["9114"],"URL":"https:\/\/doi.org\/10.1007\/s11047-009-9114-3","relation":{},"ISSN":["1567-7818","1572-9796"],"issn-type":[{"value":"1567-7818","type":"print"},{"value":"1572-9796","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,3]]}}}