caa a22 4500 605475288 CHVBK 20210128100351.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10516-015-9269-8 doi (NATIONALLICENCE)springer-10.1007/s10516-015-9269-8 Livadas Stathis Messologiou 66, 26222, Patras, Greece aut The Subjective Roots of Forcing Theory and Their Influence in Independence Results [Elektronische Daten] [Stathis Livadas] 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. Springer Science+Business Media Dordrecht, 2015 Absoluteness nationallicence Actual infinity nationallicence Completed whole nationallicence Forcing theory nationallicence Generic set nationallicence Intentional consciousness nationallicence Ordinals nationallicence Relative consistency nationallicence Subjective origin nationallicence Axiomathes Springer Netherlands 25/4(2015-12-01), 433-455 1122-1151 25:4<433 2015 25 10516 https://doi.org/10.1007/s10516-015-9269-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10516-015-9269-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Livadas Stathis Messologiou 66, 26222, Patras, Greece aut NATIONALLICENCE 773 0- Axiomathes Springer Netherlands 25/4(2015-12-01), 433-455 1122-1151 25:4<433 2015 25 10516