Boolean-valued second-order logic

Daisuke Ikegami, Jouko Väänänen

研究成果: Article査読

2 被引用数 (Scopus)

抄録

In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its validity is absolute under forcing, and its Hanf and Löwenheim numbers are smaller than those of full second-order logic.

本文言語English
ページ(範囲)167-190
ページ数24
ジャーナルNotre Dame Journal of Formal Logic
56
1
DOI
出版ステータスPublished - 2015
外部発表はい

ASJC Scopus subject areas

  • Logic

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