Definable quantifiers in second order arithmetic and elementary extensions of ω-models

When the pre-theoretical notion that is to be formalized is that of logical consequence, incompleteness alone cannot serve as an argument to disqualify a system as a proper logic,

◮ Understood more about the fine structure of countable arithmetically saturated

and Slov´ ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. [3] Vaˇ sik, P., Connections on higher order principal

Ibrahim, On existence of monotone solutions for second-order non-convex differential inclusions in infinite dimensional spaces, Portugaliae Mathematica 61 (2) (2004), 231–143..

Therefore, using the well known theorem on the continuity of the improper integral with respect to param- eters, we get the continuity of the mapping (14) at (h 0 , t 0 )..

The following observation together with Lemma 1.4 shows that in the case of an arithmetically saturated model M , intersticial gaps are strictly smaller than interstices

The extension M ≺ cof K has the automorphism exten- sion property (AEC for short) iff for every g ∈ Aut(M), if g and g −1 send coded subsets onto coded ones, then g is extendable to

This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by