Transductions in arithmetic

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• 作者：Albert Visser¹ ; ^{a.visser@uu.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：03B25 ; 03F25 ; 03F30 ; 03F45
• 刊名：Annals of Pure and Applied Logic
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：167
• 期：3
• 页码：211-234
• 全文大小：537 K

文摘

In this paper we study a new relation between sentences: transducibility. The idea of transducibility is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. Transducibility is based on a converse of Feferman's Theorem: if a sentence is interpretable over a theory U, it is, in a sense that we will explain, an inconsistency statement for U over U.

We show that, for a wide class of theories U, transducibility coincides with interpretability over U   and, for an even wider class, it coincides with Π₁${\mathrm{\Pi }}_1$-conservativity over U  . Thus, transducibility provides a new way of looking at interpretability and Π₁${\mathrm{\Pi }}_1$-conservativity. On the other hand, we will show that transducibility admits variations that are distinct from interpretability and Π₁${\mathrm{\Pi }}_1$-conservativity.

We show that transducibility satisfies the interpretability logic ILM.