Construction of A Lattice on the completion space of an algebra and an isomorphism to its Caratheodory Extension

Models of PA: when two elements are necessarily order automorphic

We hope to see how much for a model M of some completion T of PA (Peano Arithmetic) does M restriction {<} determine M, say up to isomorphism. We advance in characterizing for non-standard models M of PA the "minimal" set {(a,b):n < a < b for n in N and the linear orders {c:c <_M a}, {c:c <_M b} are isomorphic}, in particular include {(a,b): for no c in M for every n in N we have M models (forall n in N)(exists c)[2 < c^n < a wedge b < a c^n]} and for some model is equal to {(a,b):a < b < a^n for some n in N}.

T-凸性、弱即时类型和T-λ球面完备化 of o-最小结构

$T$-convexity, Weakly Immediate Types, and $T$-$λ$-Spherical Completions of o-minimal Structures

本文研究了T-凸性、弱即时类型和T-λ球面完备化，证明了T_convex理论的球面完备性及相关性质。