MINIMUM MODELS OF SECOND-ORDER SET THEORIES

Author:

WILLIAMS KAMERYN J.

Abstract

AbstractIn this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented with the principle of Elementary Transfinite Recursion. The main results are the following. (1) A countable model of ZFC has a minimum GBC-realization if and only if it admits a parametrically definable global well order. (2) Countable models of GBC admit minimal extensions with the same sets. (3) There is no minimum transitive model of KM. (4) There is a minimum β-model of GB+ETR. The main question left unanswered by this article is whether there is a minimum transitive model of GB+ETR.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference30 articles.

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. NON-TIGHTNESS IN CLASS THEORY AND SECOND-ORDER ARITHMETIC;The Journal of Symbolic Logic;2023-06-13

2. VARIETIES OF CLASS-THEORETIC POTENTIALISM;The Review of Symbolic Logic;2023-05-22

3. End extending models of set theory via power admissible covers;Annals of Pure and Applied Logic;2022-08

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