Models of weak theories of truth

Models of weak theories of truth In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$ P A . Let $${\mathfrak {Th}}$$ Th denote the class of models of $$ PA $$ P A which admit an expansion to a model of theory $${ Th}$$ T h . We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ PA ⊃ TB ⊃ RS ⊃ UTB ⊇ CT - , where $${\mathfrak {PA}}$$ PA denotes simply the class of all models of $$ PA $$ P A and $${\mathfrak {RS}}$$ RS denotes the class of recursively saturated models of $$ PA $$ P A . Our main original result is that every model of $$ PA $$ P A which admits an expansion to a model of $$ CT ^-$$ C T - , admits also an expansion to a model of $$ UTB $$ U T B . Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$ UTB $$ U T B is not relatively interpretable in $$ TB $$ T B , thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010). Archive for Mathematical Logic Springer Journals

Models of weak theories of truth

Loading next page...
Springer Berlin Heidelberg
Copyright © 2017 by The Author(s)
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial