Title | Reuniting the Antipodes โ Constructive and Nonstandard Views of the Continuum [electronic resource] : Symposium Proceedings, San Servolo, Venice, Italy, May 16-22, 1999 / edited by Peter Schuster, Ulrich Berger, Horst Osswald |
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Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-94-015-9757-9 |
Descript | XIII, 329 p. online resource |
Nonstandard construction of stable type Euclidean random field measures -- The continuum in smooth infinitesimal analysis -- Constructive unbounded operators -- The points of (locally) compact regular formal topologies -- Embedding a linear subset of ร(H) in the dual of its predual -- Nonstandard analysis by means of ideal values of sequences -- Nilpotent infinitesimals and synthetic differential geometry in classical logic -- On hyperfinite approximations of the field R -- Various continuity properties in constructive analysis -- Loeb measures and Borel algebras -- On Brouwerian bar induction -- Curt Schmiedenโs approach to infinitesimals. An eye-opener to the historiography of analysis -- A sequent calculus for constructive ordered fields -- The Puritz order and its relationship to the Rudin-Keisler order -- Unifying constructive and nonstandard analysis -- Positive lattices -- Constructive mathematics without choice -- Pointwise differentiability -- On Conway numbers and generalized real numbers -- The constructive content of nonstandard measure existence proofsโis there any? -- Kruskalโs tree theorem in a constructive theory of inductive definitions -- Real numbers and functions exhibited in dialogues -- WIJN/On the quantitative structure of ?20 -- Understanding and using Brouwerโs continuity principle -- Peirce and the continuum from a philosophical point of view