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Mekler's Construction and the Preservation of NCTP and NBTP

JinHoo Ahn, Joonhee Kim

Abstract

We give criteria for a first-order theory to be NCTP or NBTP using tree-indiscernibility. As an application, we show that Mekler's construction preserves NCTP and NBTP.

Mekler's Construction and the Preservation of NCTP and NBTP

Abstract

We give criteria for a first-order theory to be NCTP or NBTP using tree-indiscernibility. As an application, we show that Mekler's construction preserves NCTP and NBTP.
Paper Structure (7 sections, 8 theorems, 7 equations, 1 figure)

This paper contains 7 sections, 8 theorems, 7 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Tree language and tree properties
  4. Generalized indiscernibles
  5. Mekler's construction
  6. Mekler's construction of NCTP theories
  7. Mekler's construction of NBTP theories

Key Result

Theorem 3.1

The following are equivalent.

Figures (1)

  • Figure 2.4.1: Relations between dividing lines

Theorems & Definitions (31)

  • Definition 2.2
  • Definition 2.3
  • Definition 2.5
  • Definition 2.6
  • Definition 2.10
  • Definition 2.12
  • Definition 2.14
  • Definition 2.15
  • Definition 2.16
  • Definition 2.18
  • ...and 21 more