Topic Archive: Peano Arithemtic
I will discuss more work of Kaufmann and Schmerl around loftiness. In particular I will discuss how in the definition of e-loftiness we may restrict our attention to only those types that define cuts. These consideration lead to a simple proof of a theorem of Pabion’s that for kappa an uncountable cardinal a model M of PA is kappa-saturated if and only if its underlying ordering is kappa-saturated. Time permitting I will also discuss how for countable models M, being lofty is equivalent to having a recursively saturated simple extension.