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Re: Few questions on forcing, large cardinals
Posted:
Mar 19, 2013 4:12 AM


On 3/19/2013 2:18 AM, Ross A. Finlayson wrote: > > > http://math.bu.edu/people/aki/14.pdf > > "Rather, the focus is on the connections between the combinatorial > properties of the partial order of conditions and structural > properties of the extension." > > > "With forcing so expanded into the interstices of set theory and the > method so extensively amended from the beginning, what is the "it" of > Cohen's forcing and his individual achievement? Cohen discovered a > concrete and widely applicable means of operationally extending a > standard model of set theory to another without altering the ordinals. > The central technical innovation was the definable forcing relation, > through which satisfaction for the extension could be approached in > the ground model. Cohen's achievement was thus to be able to secure > properties of new sets without having all of their members in hand and > more broadly, to separate and then interweave truth and existence." >
On page 360 he speaks of having to think of truth in new way.
One result of forcing has been to consider "truth persistence under forcing". To the best of my knowledge, this typifies some of Woodin's work.
"Partiality, Truth, and Persistence" by Langholm
http://books.google.com/books?id=AOGpRxZyfFYC&pg=PA43&lpg=PA43&dq=truth+persistence&source=bl&ots=DQ5YDVLvbR&sig=O42ZBaI_H1pxsc640_83EVEKDk&hl=en&sa=X&ei=4RdIUZLuKrY2AXL9IDwAg&ved=0CFUQ6AEwBjgK
Some information about "names" and "descriptions" in relation to presupposition and the strong Kleene truth definition used by Langholm
http://plato.stanford.edu/entries/presupposition/#LocConDynTur
And yes, forcing is unobjectionable when you redefine truth.
But, no one told anyone.



