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pro vyhledávání: '"Stephen G. Simpson"'
Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work
Autor:
Stephen G. Simpson
Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core ma
Autor:
Stephen G. Simpson
Publikováno v:
The Legacy of Kurt Schütte ISBN: 9783030494230
Historically, mathematics has often been regarded as a role model for all of science—a paragon of abstraction, logical precision, and objectivity. The 19th and early 20th centuries saw tremendous progress. The great mathematician David Hilbert prop
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3e2941305db172e8a791065361788655
https://doi.org/10.1007/978-3-030-49424-7_20
https://doi.org/10.1007/978-3-030-49424-7_20
Publikováno v:
The Journal of Symbolic Logic. 82:576-589
Let $S$ be the group of finitely supported permutations of a countably infinite set. Let $K[S]$ be the group algebra of $S$ over a field $K$ of characteristic $0$. According to a theorem of Formanek and Lawrence, $K[S]$ satisfies the ascending chain
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::234c626c96a953a2b177ca8473bd6a31
https://doi.org/10.1017/jsl.2016.17
https://doi.org/10.1017/jsl.2016.17
Autor:
Stephen G. Simpson, Sankha S. Basu
Publikováno v:
Computability. 5:29-47
In this paper we study a model of intuitionistic higher-order logic which we call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the category of sheaves of sets over the topological space consisting of the Turing degrees, where
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3896278d27c5b7e618d470f3db7d673
https://doi.org/10.3233/com-150041
https://doi.org/10.3233/com-150041
Autor:
Stephen G. Simpson, Frank Stephan
Publikováno v:
Annals of Pure and Applied Logic. 166:713-728
Let X be an infinite sequence of 0's and 1's. Let f be a computable function. Recall that X is strongly f-random if and only if the a priori Kolmogorov complexity of each finite initial segment τ of X is bounded below by f ( τ ) minus a constant. W
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::224905f3408478c7efcfa420aa9ce176
https://doi.org/10.1016/j.apal.2015.03.001
https://doi.org/10.1016/j.apal.2015.03.001
Autor:
Stephen G. Simpson, Julia F. Knight
Publikováno v:
Reverse Mathematics 2001
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6be17d6b7da6b8bc522e5b8257132234
https://doi.org/10.1017/9781316755846.017
https://doi.org/10.1017/9781316755846.017
Autor:
Stephen G. Simpson, Andrew Arana
Publikováno v:
Reverse Mathematics 2001
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8bf81716ef571b3bbe818288c703dd3
https://doi.org/10.1017/9781316755846.002
https://doi.org/10.1017/9781316755846.002
Publikováno v:
Reverse Mathematics 2001
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::46b7c8473d7a867b0216af4be44995fe
https://doi.org/10.1017/9781316755846.010
https://doi.org/10.1017/9781316755846.010
Publikováno v:
Reverse Mathematics 2001
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4bdd164fb416a4751ac9847503b266ea
https://doi.org/10.1017/9781316755846.024
https://doi.org/10.1017/9781316755846.024