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Corrigendum & Addendum to "Categoricity-like Properties in the First Order Realm"

Ali Enayat, Mateusz Łełyk

Abstract

This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).

Corrigendum & Addendum to "Categoricity-like Properties in the First Order Realm"

Abstract

This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Paper Structure (4 sections, 5 theorems, 6 equations)

This paper contains 4 sections, 5 theorems, 6 equations.

Table of Contents

  1. Introduction
  2. Correction to Theorem 39 of Enayat_Łełyk_2024
  3. Correction to Theorem 77 of Enayat_Łełyk_2024
  4. Recent advances

Key Result

Theorem 1

If $\mathsf{ZF}$ is consistent, then for each $n\in\omega$ the following hold:

Theorems & Definitions (11)

  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • proof : Proof of Theorem \ref{['Set_theoretical_analogue_of_Paris_Kirby']}
  • Lemma 4
  • proof
  • proof : Proof of Theorem \ref{['N_and_K_n_are_biint_for_ZF+V=L']}
  • Remark 5
  • Claim 6: Incorrect
  • ...and 1 more