Inexhaustibility: A Non-Exhaustive Treatment Export

@book{fran:inex04, abstract = {G\"{o}dels Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. <P>Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. <P>All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough.}, author = {Franzen, Torkel}, citeulike-article-id = {798681}, citeulike-linkout-0 = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/1568811748}, citeulike-linkout-1 = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21&amp;path=ASIN/1568811748}, citeulike-linkout-2 = {http://www.amazon.fr/exec/obidos/redirect?tag=citeulike06-21&amp;path=ASIN/1568811748}, citeulike-linkout-3 = {http://www.amazon.co.uk/exec/obidos/ASIN/1568811748/citeulike00-21}, citeulike-linkout-4 = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/1568811748}, citeulike-linkout-5 = {http://www.worldcat.org/isbn/1568811748}, citeulike-linkout-6 = {http://books.google.com/books?vid=ISBN1568811748}, citeulike-linkout-7 = {http://www.amazon.com/gp/search?keywords=1568811748&index=books&linkCode=qs}, citeulike-linkout-8 = {http://www.librarything.com/isbn/1568811748}, day = {08}, howpublished = {Hardcover}, isbn = {1568811748}, keywords = {logic, mathematics, pnc, prooftheory}, month = {September}, posted-at = {2006-08-13 11:36:45}, priority = {3}, publisher = {Association for Symbolic Logic}, series = {Lecture Notes in Logic}, title = {Inexhaustibility: A Non-Exhaustive Treatment}, url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/1568811748}, volume = {16}, year = {2004} }

TY - BOOK ID - fran:inex04 L3 - citeulike-article-id:798681 N2 - Gödels Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. <P>Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. <P>All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough. SE - Lecture Notes in Logic SN - 1568811748 TI - Inexhaustibility: A Non-Exhaustive Treatment PB - Association for Symbolic Logic VL - 16 KW - logic KW - mathematics KW - pnc KW - prooftheory AU - Franzen, Torkel PY - 2004/09/08/ UR - http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20&amp;path=ASIN/1568811748 ER -