S. Feferman, Weyl Vindicated: Das Kontinuum seventy years later, in In the Light of Logic, Oxford University press, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....On the other side the intuitionists led by Brouwer were militantly against any form of actual in nite. In the middle, at least before his defection to Brouwer, stood H. Weyl who was inspired by the predicativism of H. Poincar e who accepted PA as true. Weyl in his seminal work Das Kontinuum [19, 4] was a forerunner of a ourishing and aesthetically pleasing school in the modern foundations of mathematics known as Reverse mathematics [15] Weyl s formal system can be identi ed with the basic theory of Reverse mathematics, a subsystem of second order arithmetic ACA 0 which is conservative ....

....Zermelo set theory (ZF) without the Replace2 ment axiom of Fraenkel whose model is the set V 2 of the cumulative hierarchy of sets. Anything stronger is to be looked upon as mathematical recreation without ontological rights . The modern formulation is the system W (after Weyl) of S. Feferman [4] which is conservative over PA and for which its author claims with a good reason that all scienti cally applicable analysis can be developed in it . Mathematics in W is more natural than in ACA 0 which is interpretable in W. The reason is that function spaces are de nable in W but must be ....

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S. Feferman, Weyl Vindicated: Das Kontinuum seventy years later, in In the Light of Logic, Oxford University press, 1998.

....strong, but nevertheless PRA reducible, systems in all nite types emphasizing the need of third order variables already for a faithful formalization of continuous functions between Polish spaces. Let us recall very brie y some of the history of research on 1) As Feferman pointed out in [7], Hermann Weyl initiated a program for the arithmetical foundation of mathematics in his book Das Kontinuum ( 39] In this book, Weyl observed that large parts of analysis can be developed on the basis of arithmetical comprehension. This theme was further developed in the 50 s by P. Lorenzen ....

....contains a strong uniform ( explicit ) version of arithmetical comprehension via a non constructive operator. These features hold in an even stronger form for theories with exible (variable) types which were developed successively by Feferman in his framework of explicit mathematics in [4] 6] [7] culminating in a formal system called W (where W stands for Weyl ) which was shown to be proof theoretically reducible to and conservative over PA in [11] The enormous mathematical power and exibility of the system W led Feferman in [9] to the formulation of the thesis that all (or almost ....

Feferman, S., Weyl vindicated: Das Kontinuum seventy years later, in: Cellucci, C., Sambin, G. (eds.), Temi e prospettive della logica e della loso a della scienza contemporance, vol. I, pp. 59-93 (1988), CLUEB, Bologna. Reprinted (with minor additions) in [10].

....necessary to address the question of how closely various representations of anaytical objects correspond to their ordinary mathematical definitions and to develop a general theory of representations. Let us recall very briefly some of the history of research on 1) As Feferman pointed out in [7], Hermann Weyl initiated a program for the arithmetical foundation of mathematics in his book Das Kontinuum ( 40] In this book, Weyl observed that large parts of analysis can be developed on the basis of arithmetical comprehension. This theme was further developed in the 50 s by P. Lorenzen ....

....contains a strong uniform ( explicit ) version of arithmetical comprehension via a non constructive operator. These features hold in an even stronger form for theories with flexible (variable) types which were developed successively by Feferman in his framework of explicit mathematics in [4] 6] [7] culminating in a formal system called W (where W stands for Weyl ) which was shown to be proof theoretically reducible to and conservative over PA in [11] The enormous mathematical power and flexibility of the system W led Feferman in [9] to the formulation of the thesis that all (or almost ....

Feferman, S., Weyl vindicated: Das Kontinuum seventy years later, in: Cellucci, C., Sambin, G. (eds.), Temi e prospettive della logica e della filosofia della scienza contemporance, vol. I, pp. 59-93 (1988), CLUEB, Bologna. Reprinted (with minor additions) in

....necessary to address the question of how closely various representations of anaytical objects correspond to their ordinary mathematical definitions and to develop a general theory of representations. Let us recall very briefly some of the history of research on 1) As Feferman pointed out in [7], Hermann Weyl initiated a program for the arithmetical foundation of mathematics in his book Das Kontinuum ( 39] In this book, Weyl observed that large parts of analysis can be developed on the basis of arithmetical comprehension. This theme was further developed in the 50 s by P. Lorenzen ....

....contains a strong uniform ( explicit ) version of arithmetical comprehension via a nonconstructive operator. These features hold in an even stronger form for theories with flexible (variable) types which were developed successively by Feferman in his framework of explicit mathematics in [4] 6] [7] culminating in a formal system called W (where W stands for Weyl ) which was shown to be proof theoretically reducible to and conservative over PA in [11] The enormous mathematical power and flexibility of the system W led Feferman in [9] to the formulation of the thesis that all (or almost ....

Feferman, S., Weyl vindicated: Das Kontinuum seventy years later, in: Cellucci, C., Sambin, G. (eds.), Temi e prospettive della logica e della filosofia della scienza contemporance, vol. I, pp. 59-93 (1988), CLUEB, Bologna. Reprinted (with minor additions) in [10].

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