NDLI: The Subjective Roots of Forcing Theory and Their Influence in Independence Results

Content Provider	Springer Nature Link
Author	Livadas, Stathis
Copyright Year	2015
Abstract	This article attempts a subjectively based approach, in fact one phenomenologically motivated, toward some key concepts of forcing theory, primarily the concepts of a generic set and its global properties and the absoluteness of certain fundamental relations in the extension to a forcing model M[G]. By virtue of this motivation and referring both to the original and current formulation of forcing I revisit certain set-theoretical notions serving as underpinnings of the theory and try to establish their deeper subjectively founded content and also their influence in reaching relative consistency results by the forcing method. In this perspective, the present approach may be seen as offering an alternative view of the consistency results of K. Gödel and P. Cohen in mathematical foundations reaching a subjective level that may be taken as ultimately conditioning the non-decidability of key infinity statements (such as the Continuum Hypothesis) on the level of formal theory.
Starting Page	433
Ending Page	455
Page Count	23
File Format	PDF
ISSN	11221151
Journal	Axiomathes
Volume Number	25
Issue Number	4
e-ISSN	15728390
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-04-30
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Absoluteness Actual infinity Completed whole Forcing theory Generic set Intentional consciousness Ordinals Relative consistency Subjective origin Philosophy Ontology Linguistics Cognitive Psychology Logic
Content Type	Text
Resource Type	Article
Subject	Philosophy Mathematics

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