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Set theory, arithmetic, and foundations of mathematics : theorems, philosophies / edited by Juliette Kennedy, Roman Kossak
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Lecture notes in logic ; 36Verlag: Cambridge : Cambridge University Press, 2011Beschreibung: 1 Online-Ressource (xiii, 227 pages) : digital, PDF file(s)ISBN:- 9780511910616
- Set Theory, Arithmetic, & Foundations of Mathematics
- 510
- QA248
Inhalte:
Zusammenfassung: This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.Original version: Originalfassung: 2011PPN: PPN: 883349418Package identifier: Produktsigel: ZDB-20-CTM | ZDB-20-CBO | ZDB-20-CHS
Historical remarks on Suslin's problem / Akihiro Kanamori
The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture / W. Hugh Woodin
[omega]-Models of finite set theory / Ali Enayat and James H. Schmerl and Albert Visser
Tennenbaum's theorem for models of arithmetic / Richard Kaye
Hierarchies of subsystems of weak arithmetic / Shahram Mohsenipour
Diophantine correct open induction / Sidney Raffer
Tennenbaum's theorem and recursive reducts / James H. Schmerl
History of constructivism in the 20th century / A.S. Troelstra
A very short history of ultrafinitism / Rose M. Cherubin and Mirco A. Mannucci
Sue Toledo's notes of her conversations with Gödel in 1972-1975 / Sue Toledo
Stanley Tennenbaum's Socrates / Curtis Franks
. Tennenbaum's proof of the irrationality of [the square root of] 2́ / Jouko Väänänen.
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2011