Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Second-order Version of Morley's Theorem on the Number of Countable Models does not Require Large Cardinals

Franklin D. Tall, Jing Zhang

Abstract

The consistency of a second-order version of a theorem of Morley on the number of countable models was proved in arXiv:2107.07636 with the aid of large cardinals. We here dispense with them.

The Second-order Version of Morley's Theorem on the Number of Countable Models does not Require Large Cardinals

Abstract

The consistency of a second-order version of a theorem of Morley on the number of countable models was proved in arXiv:2107.07636 with the aid of large cardinals. We here dispense with them.
Paper Structure (2 sections, 11 theorems, 3 equations)

This paper contains 2 sections, 11 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. Acknowledgment

Key Result

Theorem 1.1

Let $T$ be a first-order theory (or more generally, a sentence of $L_{\omega_1, \omega}$) in a countable signature. Then either $T$ has at most $\aleph_1$ isomorphism classes of countable models, or there is a perfect set of non-isomorphic countable models of $T$.

Theorems & Definitions (25)

  • Theorem 1.1: Absolute Morley
  • Theorem 1.2
  • Theorem : Theorem A
  • Theorem : Theorem C
  • Theorem 1.3
  • Theorem : Theorem B
  • Definition 1.4
  • Definition 1.5
  • Lemma 1.6
  • Remark 1.7
  • ...and 15 more