Tame Sets in Homogeneous Spaces

Conormal Cycles of Tame Sets

This is an exposition of Bernig’s work on the conormal cycle of a tame set. CONTENTS Introduction 1 1. Constructible functions 2 2. The Radon transform 4 3. Drop maps of constructible functions 5 4. Support functions of tame, conical Lagrangian cycles 10 5. The conormal cycle 14 Appendix A. Subanalytic currents 20 Appendix B. Indices of stratified Morse functions 22 References 25 INTRODUCTION T...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Tame Theories with Hyperarithmetic Homogeneous Models

A tame theory is a decidable first-order theory with only countably many countable models, and all complete types recursive. It is shown here that the recursive complexity of countable homogeneous models of tame theories is unbounded in the hyperarithmetic hierarchy. Recursive model theory considers model-theoretic objects and constructions from the point of view of recursion-theoretic complexi...

Convolution and Homogeneous Spaces

Homogeneously Suslin sets in tame mice

This paper studies homogeneously Suslin (hom) sets of reals in tame mice. The following results are established: In 0¶ the hom sets are precisely the ̃ 11 sets. In Mn every hom set is correctly ̃ 1n+1, and (δ + 1)-universally Baire where δ is the least Woodin. In Mω every hom set is <λ-hom, where λ is the supremum of the Woodins. §