Found 37 Documents (Results 1–37)
Infinite natural numbers: an unwanted phenomenon, or a useful concept? (English) Zbl 1261.03177
Peliš, Michal (ed.) et al., The Logica yearbook 2010. Proceedings of the 24th annual international Logica symposium, Hejnice Monastery, Czech Republic, June 21–25, 2010. London: College Publications (ISBN 978-1-84890-038-7/pbk). 283-294 (2011).
MSC:
03H15
Radically elementary analysis of an interacting particle system at an unstable equilibrium. (English) Zbl 1277.60184
Using grossone to count the number of elements of infinite sets and the connection with bijections. (English) Zbl 1259.03064
A non-standard semantics for Kahn networks in continuous time. (English) Zbl 1247.68182
Bezem, Marc (ed.), Computer science logic (CSL’11). 25th international workshop, 20th annual conference of the EACSL, Bergen, Norway, September 12–15, 2011. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-32-3). LIPIcs – Leibniz International Proceedings in Informatics 12, 35-50, electronic only (2011).
Natural numbers and infinitesimals. (English) Zbl 1258.03094
DeVidi, David (ed.) et al., Logic, mathematics, philosophy: vintage enthusiasms. Essays in honour of John L. Bell. Berlin: Springer (ISBN 978-94-007-0213-4/hbk; 978-94-007-0214-1/ebook). The Western Ontario Series in Philosophy of Science 75, 255-286 (2011).
Reviewer: Isaac Goldbring (Chicago)
Euler’s continuum functorially vindicated. (English) Zbl 1251.03098
DeVidi, David (ed.) et al., Logic, mathematics, philosophy: Vintage enthusiasms. Essays in honour of John L. Bell. Berlin: Springer (ISBN 978-94-007-0213-4/hbk; 978-94-007-0214-1/ebook). The Western Ontario Series in Philosophy of Science 75, 249-254 (2011).
Tennenbaum’s theorem and recursive reducts. (English) Zbl 1248.03055
Kennedy, Juliette (ed.) et al., Set theory, arithmetic, and foundations of mathematics. Theorems, philosophies. Cambridge: Cambridge University Press; Ithaca, NY: Association of Symbolic Logic (ASL) (ISBN 978-1-107-00804-5/hbk). Lecture Notes in Logic 36, 112-149 (2011).
Reviewer: Roman Kossak (New York)
Diophantine correct open induction. (English) Zbl 1255.03053
Kennedy, Juliette (ed.) et al., Set theory, arithmetic, and foundations of mathematics. Theorems, philosophies. Cambridge: Cambridge University Press; Ithaca, NY: Association of Symbolic Logic (ASL) (ISBN 978-1-107-00804-5/hbk). Lecture Notes in Logic 36, 93-111 (2011).
Reviewer: Roman Kossak (New York)
Hierarchies of subsystems of weak arithmetic. (English) Zbl 1252.03135
Kennedy, Juliette (ed.) et al., Set theory, arithmetic, and foundations of mathematics. Theorems, philosophies. Cambridge: Cambridge University Press; Ithaca, NY: Association of Symbolic Logic (ASL) (ISBN 978-1-107-00804-5/hbk). Lecture Notes in Logic 36, 80-92 (2011).
Reviewer: Roman Kossak (New York)
Tennenbaum’s theorem for models of arithmetic. (English) Zbl 1250.03058
Kennedy, Juliette (ed.) et al., Set theory, arithmetic, and foundations of mathematics. Theorems, philosophies. Cambridge: Cambridge University Press; Ithaca, NY: Association of Symbolic Logic (ASL) (ISBN 978-1-107-00804-5/hbk). Lecture Notes in Logic 36, 66-79 (2011).
Reviewer: Roman Kossak (New York)
The arithmetic of trees. (English) Zbl 1233.05088
50 years of non-standard analysis. (50 Jahre Nichtstandard-Analysis.) (German) Zbl 1241.26025
Reviewer: Isaac Goldbring (Los Angeles)
Exploring the foundations of discrete analytical geometry in Isabelle/HOL. (English) Zbl 1350.68232
Schreck, Pascal (ed.) et al., Automated deduction in geometry. 8th international workshop, ADG 2010, Munich, Germany, July 22–24, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-25069-9/pbk). Lecture Notes in Computer Science 6877. Lecture Notes in Artificial Intelligence, 34-50 (2011).
A set of axioms for nonstandard extensions. (English) Zbl 1235.26019
Reviewer: Isaac Goldbring (Los Angeles)
A note on parameter free \(\Pi _{1}\)-induction and restricted exponentiation. (English) Zbl 1238.03048
Reviewer: Roman Kossak (New York)
Comments on Edward Nelson’s “Internal set theory: a new approach to nonstandard analysis”. (English) Zbl 1435.03082
Independence results for variants of sharply bounded induction. (English) Zbl 1230.03091
Reviewer: Roman Kossak (New York)
The provably terminating operations of the subsystem PETJ of explicit mathematics. (English) Zbl 1238.03039
Reviewer: Roman Murawski (Poznań)
Quadratic forms in models of \(I\Delta_0 + \Omega_1\). II: Local equivalence. (English) Zbl 1230.03090
Reviewer: Roman Kossak (New York)
Fermat-Reyes method in the ring of Fermat reals. (English) Zbl 1238.03052
Reviewer: Isaac Goldbring (Los Angeles)
Hyperreal expected utilities and Pascal’s wager. (English) Zbl 1238.03013
Reviewer: Roman Murawski (Poznań)
Programming with infinitesimals: a While-language for hybrid system modeling. (English) Zbl 1333.68181
Aceto, Luca (ed.) et al., Automata, languages and programming. 38th international colloquium, ICALP 2011, Zurich, Switzerland, July 4–8, 2011. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-22011-1/pbk). Lecture Notes in Computer Science 6756, 392-403 (2011).
A potential subtlety concerning the distinction between determinism and nondeterminism. (English) Zbl 1269.03017
Heller, Michael (ed.) et al., Infinity. New research frontiers. Based on the conference on new frontiers in research on infinity, San Marino, August 18–20, 2006. Cambridge: Cambridge University Press (ISBN 978-1-107-00387-3/hbk). 119-129 (2011).
ERNA and Friedman’s reverse mathematics. (English) Zbl 1231.03059
Reviewer: Emil Jeřábek (Praha)
Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus. arXiv:1109.2098
Preprint, arXiv:1109.2098 [math.HO] (2011).
Nonstandard Analysis in Topology. arXiv:1107.3323
Preprint, arXiv:1107.3323 [math.GN] (2011).
Another Proof of the Existence a Dedekind Complete Totally Ordered Field. arXiv:1101.3825
Preprint, arXiv:1101.3825 [math.LO] (2011).
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