The Subjective Roots of Forcing Theory and Their Influence in Independence Results
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| 024 | 7 | 0 | |a 10.1007/s10516-015-9269-8 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10516-015-9269-8 | ||
| 100 | 1 | |a Livadas |D Stathis |u Messologiou 66, 26222, Patras, Greece |4 aut | |
| 245 | 1 | 4 | |a The Subjective Roots of Forcing Theory and Their Influence in Independence Results |h [Elektronische Daten] |c [Stathis Livadas] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2015 | ||
| 690 | 7 | |a Absoluteness |2 nationallicence | |
| 690 | 7 | |a Actual infinity |2 nationallicence | |
| 690 | 7 | |a Completed whole |2 nationallicence | |
| 690 | 7 | |a Forcing theory |2 nationallicence | |
| 690 | 7 | |a Generic set |2 nationallicence | |
| 690 | 7 | |a Intentional consciousness |2 nationallicence | |
| 690 | 7 | |a Ordinals |2 nationallicence | |
| 690 | 7 | |a Relative consistency |2 nationallicence | |
| 690 | 7 | |a Subjective origin |2 nationallicence | |
| 773 | 0 | |t Axiomathes |d Springer Netherlands |g 25/4(2015-12-01), 433-455 |x 1122-1151 |q 25:4<433 |1 2015 |2 25 |o 10516 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10516-015-9269-8 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10516-015-9269-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Livadas |D Stathis |u Messologiou 66, 26222, Patras, Greece |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Axiomathes |d Springer Netherlands |g 25/4(2015-12-01), 433-455 |x 1122-1151 |q 25:4<433 |1 2015 |2 25 |o 10516 | ||