Matches in SemOpenAlex for { <https://semopenalex.org/work/W2058158890> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2058158890 abstract "The notion of an w-local functor is used to formulate and prove a theorem which is claimed to encompass Lefschetz's principle in algebraic geometry. In his foundational work, A. Weil formulates Lefschetz's principle as follows: For a given value of the characteristic p [=zero or a prime], every result involving only a finite number of points and of varieties, which has been proved for some choice of the universal [i.e. an algebraically closed field of characteristic p of infinite transcendence degree over the prime field] remains valid without restriction; there is but one algebraic geometry of characteristic p for each value of p, not one algebraic geometry for each universal domain ([6, p. 306]). The purpose of this paper in applied logic is to give a proof of this statement, a proof which is motivated by the typical example with which Weil follows the above statement. Weil states a theorem which he proves for the universal of complex numbers (using complex analytic methods); this is followed by an argument proving the theorem for any universal of characteristic zero, an argument which involves successive extensions of an isomorphism of finitely-generated subfields of two universal domains. This type of argument is one commonly found in logic and usually called the argument. (See [1] for an expository paper on the use of the method.) The theorem of ?1 of this paper may be regarded as a formalization of this argument to prove a general result which may be said to include Lefschetz's principle as stated above. In fact our theorem is just a special case of a theorem of Feferman [3] and our only contribution is the observation that this result has relevance for algebraic geometry. The significance-theoretical, if not practical-of our general theorem lies in the fact that the back-and-forth argument, which enables one to transfer a result from one universal to another, is done once and for all. Then to apply the general theorem to a particular result of algebraic geometry only requires a check that the particular result falls Received by the editors July 28, 1971. AMS (MOS) subject class flcations (1970). Primary 14A99, 02H15." @default.
- W2058158890 created "2016-06-24" @default.
- W2058158890 creator A5031440068 @default.
- W2058158890 date "1973-02-01" @default.
- W2058158890 modified "2023-09-26" @default.
- W2058158890 title "Lefschetz’s principle and local functors" @default.
- W2058158890 cites W1506763190 @default.
- W2058158890 cites W2062454016 @default.
- W2058158890 cites W2330009127 @default.
- W2058158890 cites W38892188 @default.
- W2058158890 cites W561395332 @default.
- W2058158890 doi "https://doi.org/10.1090/s0002-9939-1973-0325389-7" @default.
- W2058158890 hasPublicationYear "1973" @default.
- W2058158890 type Work @default.
- W2058158890 sameAs 2058158890 @default.
- W2058158890 citedByCount "4" @default.
- W2058158890 countsByYear W20581588902015 @default.
- W2058158890 countsByYear W20581588902020 @default.
- W2058158890 crossrefType "journal-article" @default.
- W2058158890 hasAuthorship W2058158890A5031440068 @default.
- W2058158890 hasBestOaLocation W20581588901 @default.
- W2058158890 hasConcept C115624301 @default.
- W2058158890 hasConcept C118615104 @default.
- W2058158890 hasConcept C134306372 @default.
- W2058158890 hasConcept C136119220 @default.
- W2058158890 hasConcept C138885662 @default.
- W2058158890 hasConcept C156772000 @default.
- W2058158890 hasConcept C17744445 @default.
- W2058158890 hasConcept C185592680 @default.
- W2058158890 hasConcept C199539241 @default.
- W2058158890 hasConcept C202444582 @default.
- W2058158890 hasConcept C203436722 @default.
- W2058158890 hasConcept C203701370 @default.
- W2058158890 hasConcept C2777026412 @default.
- W2058158890 hasConcept C2780813799 @default.
- W2058158890 hasConcept C33923547 @default.
- W2058158890 hasConcept C41895202 @default.
- W2058158890 hasConcept C55493867 @default.
- W2058158890 hasConcept C8010536 @default.
- W2058158890 hasConcept C9376300 @default.
- W2058158890 hasConcept C9652623 @default.
- W2058158890 hasConcept C98184364 @default.
- W2058158890 hasConceptScore W2058158890C115624301 @default.
- W2058158890 hasConceptScore W2058158890C118615104 @default.
- W2058158890 hasConceptScore W2058158890C134306372 @default.
- W2058158890 hasConceptScore W2058158890C136119220 @default.
- W2058158890 hasConceptScore W2058158890C138885662 @default.
- W2058158890 hasConceptScore W2058158890C156772000 @default.
- W2058158890 hasConceptScore W2058158890C17744445 @default.
- W2058158890 hasConceptScore W2058158890C185592680 @default.
- W2058158890 hasConceptScore W2058158890C199539241 @default.
- W2058158890 hasConceptScore W2058158890C202444582 @default.
- W2058158890 hasConceptScore W2058158890C203436722 @default.
- W2058158890 hasConceptScore W2058158890C203701370 @default.
- W2058158890 hasConceptScore W2058158890C2777026412 @default.
- W2058158890 hasConceptScore W2058158890C2780813799 @default.
- W2058158890 hasConceptScore W2058158890C33923547 @default.
- W2058158890 hasConceptScore W2058158890C41895202 @default.
- W2058158890 hasConceptScore W2058158890C55493867 @default.
- W2058158890 hasConceptScore W2058158890C8010536 @default.
- W2058158890 hasConceptScore W2058158890C9376300 @default.
- W2058158890 hasConceptScore W2058158890C9652623 @default.
- W2058158890 hasConceptScore W2058158890C98184364 @default.
- W2058158890 hasLocation W20581588901 @default.
- W2058158890 hasOpenAccess W2058158890 @default.
- W2058158890 hasPrimaryLocation W20581588901 @default.
- W2058158890 hasRelatedWork W1503946811 @default.
- W2058158890 hasRelatedWork W1557428790 @default.
- W2058158890 hasRelatedWork W1615470836 @default.
- W2058158890 hasRelatedWork W1727751865 @default.
- W2058158890 hasRelatedWork W1995257291 @default.
- W2058158890 hasRelatedWork W2044772876 @default.
- W2058158890 hasRelatedWork W2092613668 @default.
- W2058158890 hasRelatedWork W2179231406 @default.
- W2058158890 hasRelatedWork W2180101131 @default.
- W2058158890 hasRelatedWork W2205953921 @default.
- W2058158890 hasRelatedWork W2328623916 @default.
- W2058158890 hasRelatedWork W250298099 @default.
- W2058158890 hasRelatedWork W2522988670 @default.
- W2058158890 hasRelatedWork W2905280330 @default.
- W2058158890 hasRelatedWork W2953104099 @default.
- W2058158890 hasRelatedWork W2963418286 @default.
- W2058158890 hasRelatedWork W2963544182 @default.
- W2058158890 hasRelatedWork W3100717873 @default.
- W2058158890 hasRelatedWork W3112947914 @default.
- W2058158890 hasRelatedWork W3126703740 @default.
- W2058158890 isParatext "false" @default.
- W2058158890 isRetracted "false" @default.
- W2058158890 magId "2058158890" @default.
- W2058158890 workType "article" @default.