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Title: Satisfaction is not absolute
Speaker: Joel David Hamkins (College of Staten Island and CUNY Graduate Center)
Time: Friday, October 25, 2013 at 4:45 pm
Place: MSB 203Abstract: The satisfaction relation N satisfies phi(a), where N denotes the natural numbers, of first-order logic, it turns out, is less absolute than might have been supposed. Two models of set theory, for example, can agree on their natural numbers N and on what they think is the standard model of arithmetic, yet disagree on their theories of arithmetic truth, the first-order truths of this structure. Two models of set theory can have the same natural numbers and the same reals, yet disagree on projective truth. Two models of set theory can have the same natural numbers and a computable linear order in common, yet disagree about whether it is well-ordered. Two models of set theory can have a transitive rank initial segment V_delta in common, yet disagree about whether it is a model of ZFC. The arguments rely mainly on elementary classical methods. This is joint work with Ruizhi Yang (Shanghai). Commentary concerning this talk can be made on the speaker's blog at http://jdh.hamkins.org/satisfaction-connecticut-october-2013.Comments: Note unusual time and location!